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United States Patent Application 
20170294965

Kind Code

A1

ASHRAFI; SOLYMAN
; et al.

October 12, 2017

SYSTEM AND METHOD FOR COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH
MULTIPLE LAYER OVERLAY MODULATION
Abstract
A system includes first signal processing circuitry to transmit a signal
including a plurality of data streams over a link. The first signal
processing circuitry generates a plurality of composite data streams by
overlaying at least one first data signal of the plurality of data
signals in a first data layer with at least one second data signal of the
plurality of data signals in a second data layer. Second circuitry
processes the plurality of composite data streams to associate with each
of the plurality of composite data streams a function to provide
minimization of a timebandwidth product of the plurality of composite
data streams to enable transmission of each of the plurality of composite
data streams on the link at a same time.
Inventors: 
ASHRAFI; SOLYMAN; (PLANO, TX)
; LINQUIST; ROGER; (DALLAS, TX)
; ASHRAFI; NIMA; (PLANO, TX)

Applicant:  Name  City  State  Country  Type  NXGEN PARTNERS IP, LLC  Dallas  TX  US
  
Family ID:

1000002736079

Appl. No.:

15/632533

Filed:

June 26, 2017 
Related U.S. Patent Documents
            
 Application Number  Filing Date  Patent Number 

 15357808  Nov 21, 2016  9712238 
 15632533   
 15144297  May 2, 2016  9503258 
 15357808   
 14323082  Jul 3, 2014  9331875 
 15144297   
 61975142  Apr 4, 2014  

Current U.S. Class: 
1/1 
Current CPC Class: 
H04B 10/2575 20130101; H04B 10/11 20130101; H04B 10/2581 20130101; H04L 27/362 20130101; H04J 14/06 20130101; H04L 27/3405 20130101; H04L 27/366 20130101; H04B 10/5161 20130101 
International Class: 
H04B 10/2575 20060101 H04B010/2575; H04B 10/2581 20060101 H04B010/2581; H04L 27/36 20060101 H04L027/36; H04J 14/06 20060101 H04J014/06; H04L 27/34 20060101 H04L027/34; H04B 10/11 20060101 H04B010/11; H04B 10/516 20060101 H04B010/516 
Claims
1. A system, comprising: first signal processing circuitry for
transmitting a signal including a plurality of data streams over a link,
the first signal processing circuitry further comprising: first circuitry
for processing each of the plurality of input data streams to generate a
plurality of parallel pairs of data streams including an inphase stream
(I) and a quadraturephase stream (Q) for each of the plurality of input
data streams; modulating each of the plurality of parallel pairs of data
streams with a selected one of at least three mutually orthogonal
functions and each of the plurality of parallel pairs at a different
signal width, respectively, to generate a plurality of data signals, each
associated with one of the plurality of parallel pairs of data streams;
generating a plurality of composite data streams by overlaying at least
one first data signal of the plurality of data signals in a first data
layer with at least one second data signal of the plurality of data
signals in a second data layer; and second circuitry for processing the
plurality of composite data streams to associate with each of the
plurality of composite data streams a function to provide minimization of
a timebandwidth product of the plurality of composite data streams to
enable transmission of each of the plurality of composite data streams on
the link at a same time.
2. The system of claim 1, wherein the link further comprises at least one
of a fiber optic link, a multimode fiber, a free space optics link and
an RF link.
3. The system of claim 1, wherein the time bandwidth product takes a form
of 1/2(2n+1) where n is an integer ranging from 0 to infinity.
4. The system of claim 1, wherein the at least three mutually orthogonal
functions comprises a plurality of timelimited and bandlimited
functions.
5. The communications system of claim 1, wherein the at least three
mutually orthogonal functions comprises at least one of a plurality of
modified Hermite polynomials, Jacobi polynomials, Gegenbauer polynomials,
Legendre polynomials, Chebyshev polynomials and Laguerre functions.
6. The system of claim 1, wherein the at least three mutually orthogonal
functions comprises a plurality of rectangular, cylindrical, and
spherical functions.
7. The system of claim 1, further including second signal processing
circuitry for receiving the plurality of composite data streams on the
link, the second signal processing circuitry further comprising: a signal
separator for separating each of the plurality of composite data streams
having the different functions to provide minimization of the
timebandwidth product applied thereto by the second circuitry from each
other; third circuitry for removing the function to provide minimization
of the timebandwidth product of the plurality of composite data streams
applied thereto by the second circuitry from each of the plurality of
composite data streams; fourth circuitry for demodulating the plurality
of composite data streams into the plurality of input data streams.
8. A system, comprising: first signal processing circuitry for
transmitting a signal including a plurality of data streams over a link,
the first signal processing circuitry further comprising: first circuitry
for processing each of the plurality of input data streams to generate a
plurality of parallel pairs of data streams including an inphase stream
(I) and a quadraturephase stream (Q) for each of the plurality of input
data streams, modulating each of the plurality of parallel pairs of data
streams with a selected one of at least three mutually orthogonal
functions and each of the plurality of parallel pairs at a different
signal width, respectively, to generate a plurality of data signals, each
associated with one of the plurality of parallel pairs of data streams,
and generating a plurality of composite data streams by overlaying at
least one first data signal of the plurality of data signals in a first
data layer with at least one second data signal of the plurality of data
signals in a second data layer; and second circuitry for processing the
plurality of composite data streams to associate with each of the
plurality of composite data streams a function to provide minimization of
a timebandwidth product of the plurality of composite data streams to
enable transmission of each of the plurality of composite data streams on
the link at a same time; second signal processing circuitry for receiving
the signal over the link, the second signal processing circuitry further
comprising: third circuitry for removing the function to provide
minimization of the timebandwidth product of the plurality of composite
data streams applied thereto by the second circuitry from each of the
plurality of composite data streams; and fourth circuitry for
demodulating the plurality of composite data streams into the plurality
of input data streams.
9. The system of claim 8, wherein the link further comprises at least one
of a fiber optic link, a multimode fiber, a free space optics link and
an RF link
10. The system of claim 8, wherein the time bandwidth product takes a
form of 1/2(2n+1) where n is an integer ranging from 0 to infinity.
11. The system of claim 8, wherein the at least three mutually orthogonal
functions comprises at least one of a plurality of timelimited and
bandlimited functions, rectangular functions, cylindrical functions and
spherical functions.
12. The system of claim 8, wherein the at least three mutually orthogonal
functions comprises at least one of a plurality of modified Hermite
polynomials, Jacobi polynomials, Gegenbauer polynomials, Legendre
polynomials, Chebyshev polynomials and Laguerre functions.
13. A method for providing a plurality of input streams from first signal
processing circuitry to second signal processing circuitry over a link,
comprising: receiving the plurality of input streams; processing each of
the plurality of input data streams to generate a plurality of parallel
pairs of data streams including an inphase stream (I) and a
quadraturephase stream (Q) for each of the plurality of input data
streams; modulating each of the plurality of parallel pairs of data
streams with a selected one of at least three mutually orthogonal
functions and each of the plurality of parallel pairs at a different
signal width, respectively, to generate a plurality of data signals, each
associated with one of the plurality of parallel pairs of data streams,
and generating a plurality of composite data streams by overlaying at
least one first data signal of the plurality of data signals in a first
data layer with at least one second data signal of the plurality of data
signals in a second data layer; applying a function to provide
minimization of a timebandwidth product of the plurality of composite
data streams to enable transmission of each of the plurality of composite
data streams on the link at a same time; and placing the plurality of
composite data streams on the link, each of the plurality of composite
data streams having the function associated therewith to enable each of
the plurality of composite data streams on the link at a same time.
14. The method of claim 13, wherein the link further comprises at least
one of a fiber optic link, a multimode fiber, a free space optics link
and an RF link.
15. The method of claim 13, wherein the time bandwidth product takes a
form of 1/2(2n+1) where n is an integer ranging from 0 to infinity.
16. The method of claim 13, wherein the at least three mutually
orthogonal functions comprises at least one of a plurality of
timelimited and bandlimited functions, rectangular functions,
cylindrical functions and spherical functions.
17. The method of claim 13, wherein the at least three mutually
orthogonal functions comprises a plurality of at least one of modified
Hermite polynomials, Jacobi polynomials, Gegenbauer polynomials, Legendre
polynomials, Chebyshev polynomials and Laguerre functions.
18. The method of claim 13, further including: receiving the plurality of
composite data streams on the link; separating each of the plurality of
composite data streams having the different functions to provide
minimization of the timebandwidth product from each other; demodulating
the functions to provide minimization of the timebandwidth product from
each of the plurality of composite data streams; and demodulating the
plurality of composite data streams into the plurality of input data
streams.
Description
CROSSREFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent application Ser.
No. 15/357,808, filed on Nov. 21, 2016 and entitled SYSTEM AND METHOD FOR
COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAY
MODULATION (Atty. Dkt. No. NXGN33248). U.S. application Ser. No.
15/357,808 is a continuation of U.S. patent application Ser. No.
15/144,297, filed on May 2, 2016 and entitled SYSTEM AND METHOD FOR
COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAY
MODULATION (Atty. Dkt. No. NXGN32804), now U.S. Pat. No. 9,503,258,
issued on Nov. 22, 2016, which is a continuation of U.S. application Ser.
No. 14/323,082, filed on Jul. 3, 2014, entitled SYSTEM AND METHOD FOR
COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAY
MODULATION, now U.S. Pat. No. 9,331,875, issued on May 3, 2016 (Atty.
Dkt. No. NXGN32173), which claims benefit of U.S. Provisional
Application No. 61/975,142, filed Apr. 4, 2014, entitled SYSTEM AND
METHOD FOR COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MODULATION
(Atty. Dkt. No. NXGN32131). U.S. application Ser. Nos. 15/357,808,
15/144,297, 14/323,082 and 61/975,142, and U.S. Pat. No. 9,331,875 are
incorporated by reference herein in their entirety.
TECHNICAL FIELD
[0002] The following disclosure relates to systems and methods for
increasing communication bandwidth, and more particularly to increasing
communications bandwidth using a combination of the application of
orbital angular momentum to various signals, and the modulation of
signals using a multiple layer overlay modulation scheme.
BACKGROUND
[0003] The use of voice and data networks has greatly increased as the
number of personal computing and communication devices, such as laptop
computers, mobile telephones, Smartphones, tablets, et cetera, has grown.
The astronomically increasing number of personal mobile communication
devices has concurrently increased the amount of data being transmitted
over the networks providing infrastructure for these mobile communication
devices. As these mobile communication devices become more ubiquitous in
business and personal lifestyles, the abilities of these networks to
support all of the new users and user devices has been strained. Thus, a
major concern of network infrastructure providers is the ability to
increase their bandwidth in order to support the greater load of voice
and data communications and particularly video that are occurring.
Traditional manners for increasing the bandwidth in such systems have
involved increasing the number of channels so that a greater number of
communications may be transmitted, or increasing the speed at which
information is transmitted over existing channels in order to provide
greater throughput levels over the existing channel resources.
[0004] However, while each of these techniques have improved system
bandwidths, existing technologies have taken the speed of communications
to a level such that drastic additional speed increases are not possible,
even though bandwidth requirements due to increased usage are continuing
to grow exponentially. Additionally, the number of channels assigned for
voice and data communications, while increasing somewhat, have not
increased to a level to completely support the increasing demands of a
voice and data intensive use society. Thus, there is a great need for
some manner for increasing the bandwidth throughput within existing voice
and data communication that increases the bandwidth on existing voice and
data channels.
SUMMARY
[0005] The present invention, as disclosed and describe herein, in one
aspect thereof, comprises a system includes first signal processing
circuitry for transmitting a signal including a plurality of data streams
over a link. The first signal processing circuitry further includes first
circuitry for processing each of the plurality of input data streams to
generate a plurality of parallel pairs of data streams including an
inphase stream (I) and a quadraturephase stream (Q) for each of the
plurality of input data streams and for modulating each of the plurality
of parallel pairs of data streams with a selected one of at least three
mutually orthogonal functions. Each of the plurality of parallel pairs at
a different signal width, respectively, to generate a plurality of data
signals, each associated with one of the plurality of parallel pairs of
data streams. The first processing circuitry further generating a
plurality of composite data streams by overlaying at least one first data
signal of the plurality of data signals in a first data layer with at
least one second data signal of the plurality of data signals in a second
data layer. Second circuitry processes the plurality of composite data
streams to associate with each of the plurality of composite data streams
a function to provide minimization of a timebandwidth product of the
plurality of composite data streams to enable transmission of each of the
plurality of composite data streams on the link at a same time.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] For a more complete understanding, reference is now made to the
following description taken in conjunction with the accompanying Drawings
in which:
[0007] FIG. 1 illustrates various techniques for increasing spectral
efficiency within a transmitted signal;
[0008] FIG. 2 illustrates a particular technique for increasing spectral
efficiency within a transmitted signal;
[0009] FIG. 3 illustrates a general overview of the manner for providing
communication bandwidth between various communication protocol
interfaces;
[0010] FIG. 4 illustrates the manner for utilizing multiple level overlay
modulation with twisted pair/cable interfaces;
[0011] FIG. 5 illustrates a general block diagram for processing a
plurality of data streams within an optical communication system;
[0012] FIG. 6 is a functional block diagram of a system for generating
orbital angular momentum within a communication system;
[0013] FIG. 7 is a functional block diagram of the orbital angular
momentum signal processing block of FIG. 6;
[0014] FIG. 8 is a functional block diagram illustrating the manner for
removing orbital angular momentum from a received signal including a
plurality of data streams;
[0015] FIG. 9 illustrates a single wavelength having two quantispin
polarizations providing an infinite number of signals having various
orbital angular momentums associated therewith;
[0016] FIG. 10A illustrates a plane wave having only variations in the
spin angular momentum;
[0017] FIG. 10B illustrates a signal having both spin and orbital angular
momentum applied thereto;
[0018] FIGS. 11A11C illustrate various signals having different orbital
angular momentum applied thereto;
[0019] FIG. 11D illustrates a propagation of Poynting vectors for various
Eigen modes;
[0020] FIG. 11E illustrates a spiral phase plate;
[0021] FIG. 12 illustrates a multiple level overlay modulation system;
[0022] FIG. 13 illustrates a multiple level overlay demodulator;
[0023] FIG. 14 illustrates a multiple level overlay transmitter system;
[0024] FIG. 15 illustrates a multiple level overlay receiver system;
[0025] FIGS. 16A16K illustrate representative multiple level overlay
signals and their respective spectral power densities;
[0026] FIG. 17 illustrates comparisons of multiple level overlay signals
within the time and frequency domain;
[0027] FIG. 18 illustrates a spectral alignment of multiple level overlay
signals for differing bandwidths of signals;
[0028] FIG. 19 illustrates an alternative spectral alignment of multiple
level overlay signals;
[0029] FIG. 20 illustrates power spectral density for various signal
layers using a combined three layer multiple level overlay technique;
[0030] FIG. 21 illustrates power spectral density on a log scale for
layers using a combined three layer multiple level overlay modulation;
[0031] FIG. 22 illustrates a bandwidth efficiency comparison for square
root raised cosine versus multiple layer overlay for a symbol rate of
1/6;
[0032] FIG. 23 illustrates a bandwidth efficiency comparison between
square root raised cosine and multiple layer overlay for a symbol rate of
1/4;
[0033] FIG. 24 illustrates a performance comparison between square root
raised cosine and multiple level overlay using ACLR;
[0034] FIG. 25 illustrates a performance comparison between square root
raised cosine and multiple lever overlay using out of band power;
[0035] FIG. 26 illustrates a performance comparison between square root
raised cosine and multiple lever overlay using band edge PSD;
[0036] FIG. 27 is a block diagram of a transmitter subsystem for use with
multiple level overlay;
[0037] FIG. 28 is a block diagram of a receiver subsystem using multiple
level overlay;
[0038] FIG. 29 illustrates an equivalent discreet time orthogonal channel
of modified multiple level overlay;
[0039] FIG. 30 illustrates the PSDs of multiple layer overlay, modified
multiple layer overlay and square root raised cosine;
[0040] FIG. 31 illustrates a bandwidth comparison based on 40 dBc out of
band power bandwidth between multiple layer overlay and square root
raised cosine;
[0041] FIG. 32 illustrates equivalent discrete time parallel orthogonal
channels of modified multiple layer overlay;
[0042] FIG. 33 illustrates the channel power gain of the parallel
orthogonal channels of modified multiple layer overlay with three layers
and T.sub.sym=3;
[0043] FIG. 34 illustrates a spectral efficiency comparison based on ACLR1
between modified multiple layer overlay and square root raised cosine;
[0044] FIG. 35 illustrates a spectral efficiency comparison between
modified multiple layer overlay and square root raised cosine based on
OBP;
[0045] FIG. 36 illustrates a spectral efficiency comparison based on ACLR1
between modified multiple layer overlay and square root raised cosine;
[0046] FIG. 37 illustrates a spectral efficiency comparison based on OBP
between modified multiple layer overlay and square root raised cosine;
[0047] FIG. 38 illustrates a block diagram of a baseband transmitter for a
low pass equivalent modified multiple layer overlay system;
[0048] FIG. 39 illustrates a block diagram of a baseband receiver for a
low pass equivalent modified multiple layer overlay system;
[0049] FIG. 40 illustrates the configuration of an optical fiber
communication system;
[0050] FIG. 41A illustrates a single mode fiber;
[0051] FIG. 41B illustrates multicore fibers;
[0052] FIG. 41C illustrates multimode fibers;
[0053] FIG. 41D illustrates a hollow core fiber;
[0054] FIG. 42 illustrates the first six modes within a step index fiber;
[0055] FIG. 43 illustrates the classes of random perturbations within a
fiber;
[0056] FIG. 44 illustrates the intensity patterns of first order groups
within a vortex fiber;
[0057] FIGS. 45A and 45B illustrate index separation in first order modes
of a multimode fiber;
[0058] FIG. 46 illustrates a freespace communication system;
[0059] FIG. 47 illustrates a block diagram of a freespace optics system
using orbital angular momentum and multilevel overlay modulation;
[0060] FIGS. 48A48C illustrate the manner for multiplexing multiple data
channels into optical links to achieve higher data capacity;
[0061] FIG. 48D illustrates groups of concentric rings for a wavelength
having multiple OAM valves;
[0062] FIG. 49 illustrates a WDM channel containing many orthogonal OAM
beams;
[0063] FIG. 50 illustrates a node of a freespace optical system;
[0064] FIG. 51 illustrates a network of nodes within a freespace optical
system;
[0065] FIG. 52 illustrates a system for multiplexing between a free space
signal and an RF signal;
[0066] FIG. 53 illustrates a block diagram of an OAM processing system
utilizing quantum key distribution;
[0067] FIG. 54 illustrates a basic quantum key distribution system;
[0068] FIG. 55 illustrates the manner in which two separate states are
combined into a single conjugate pair within quantum key distribution;
[0069] FIG. 56 illustrates one manner in which 0 and 1 bits may be
transmitted using different basis within a quantum key distribution
system;
[0070] FIG. 57 is a flow diagram illustrating the process for a
transmitter transmitting a quantum key;
[0071] FIG. 58 illustrates the manner in which the receiver may receive
and determine a shared quantum key;
[0072] FIG. 59 more particularly illustrates the manner in which a
transmitter and receiver may determine a shared quantum key;
[0073] FIG. 60 is a flow diagram illustrating the process for determining
whether to keep or abort a determined key;
[0074] FIG. 61 illustrates a functional block diagram of a transmitter and
receiver utilizing a freespace quantum key distribution system;
[0075] FIG. 62 illustrates a network cloudbased quantum key distribution
system;
[0076] FIG. 63 illustrates a highspeed single photon detector in
communication with a plurality of users; and
[0077] FIG. 64 illustrates a nodal quantum key distribution network.
DETAILED DESCRIPTION
[0078] Referring now to the drawings, wherein like reference numbers are
used herein to designate like elements throughout, the various views and
embodiments of system and method for communication using orbital angular
momentum with modulation are illustrated and described, and other
possible embodiments are described. The figures are not necessarily drawn
to scale, and in some instances the drawings have been exaggerated and/or
simplified in places for illustrative purposes only. One of ordinary
skill in the art will appreciate the many possible applications and
variations based on the following examples of possible embodiments.
[0079] Referring now to the drawings, and more particularly to FIG. 1,
wherein there is illustrated two manners for increasing spectral
efficiency of a communications system. In general, there are basically
two ways to increase spectral efficiency 102 of a communications system.
The increase may be brought about by signal processing techniques 104 in
the modulation scheme or using multiple access technique. Additionally,
the spectral efficiency can be increase by creating new Eigen channels
106 within the electromagnetic propagation. These two techniques are
completely independent of one another and innovations from one class can
be added to innovations from the second class. Therefore, the combination
of this technique introduced a further innovation.
[0080] Spectral efficiency 102 is the key driver of the business model of
a communications system. The spectral efficiency is defined in units of
bit/sec/hz and the higher the spectral efficiency, the better the
business model. This is because spectral efficiency can translate to a
greater number of users, higher throughput, higher quality or some of
each within a communications system.
[0081] Regarding techniques using signal processing techniques or multiple
access techniques. These techniques include innovations such as TDMA,
FDMA, CDMA, EVDO, GSM, WCDMA, HSPA and the most recent OFDM techniques
used in 4G WIMAX and LTE. Almost all of these techniques use decadesold
modulation techniques based on sinusoidal Eigen functions called QAM
modulation. Within the second class of techniques involving the creation
of new Eigen channels 106, the innovations include diversity techniques
including space and polarization diversity as well as multiple
input/multiple output (MIMO) where uncorrelated radio paths create
independent Eigen channels and propagation of electromagnetic waves.
[0082] Referring now to FIG. 2, the present communication system
configuration introduces two techniques, one from the signal processing
techniques 104 category and one from the creation of new eigen channels
106 category that are entirely independent from each other. Their
combination provides a unique manner to disrupt the access part of an end
to end communications system from twisted pair and cable to fiber optics,
to free space optics, to RF used in cellular, backhaul and satellite. The
first technique involves the use of a new signal processing technique
using new orthogonal signals to upgrade QAM modulation using non
sinusoidal functions. This is referred to as quantum level overlay (QLO)
202. The second technique involves the application of new electromagnetic
wavefronts using a property of electromagnetic waves or photon, called
orbital angular momentum (QAM) 104. Application of each of the quantum
level overlay techniques 202 and orbital angular momentum application 204
uniquely offers orders of magnitude higher spectral efficiency 206 within
communication systems in their combination.
[0083] With respect to the quantum level overlay technique 202, new eigen
functions are introduced that when overlapped (on top of one another
within a symbol) significantly increases the spectral efficiency of the
system. The quantum level overlay technique 302 borrows from quantum
mechanics, special orthogonal signals that reduce the time bandwidth
product and thereby increase the spectral efficiency of the channel. Each
orthogonal signal is overlaid within the symbol acts as an independent
channel. These independent channels differentiate the technique from
existing modulation techniques.
[0084] With respect to the application of orbital angular momentum 204,
this technique introduces twisted electromagnetic waves, or light beams,
having helical wave fronts that carry orbital angular momentum (OAM).
Different OAM carrying waves/beams can be mutually orthogonal to each
other within the spatial domain, allowing the waves/beams to be
efficiently multiplexed and demultiplexed within a communications link.
OAM beams are interesting in communications due to their potential
ability in special multiplexing multiple independent data carrying
channels.
[0085] With respect to the combination of quantum level overlay techniques
202 and orbital angular momentum application 204, the combination is
unique as the OAM multiplexing technique is compatible with other
electromagnetic techniques such as wave length and polarization division
multiplexing. This suggests the possibility of further increasing system
performance. The application of these techniques together in high
capacity data transmission disrupts the access part of an end to end
communications system from twisted pair and cable to fiber optics, to
free space optics, to RF used in cellular/backhaul and satellites.
[0086] Each of these techniques can be applied independent of one another,
but the combination provides a unique opportunity to not only increase
spectral efficiency, but to increase spectral efficiency without
sacrificing distance or signal to noise ratios.
[0087] Using the Shannon Capacity Equation, a determination may be made if
spectral efficiency is increased. This can be mathematically translated
to more bandwidth. Since bandwidth has a value, one can easily convert
spectral efficiency gains to financial gains for the business impact of
using higher spectral efficiency. Also, when sophisticated forward error
correction (FEC) techniques are used, the net impact is higher quality
but with the sacrifice of some bandwidth. However, if one can achieve
higher spectral efficiency (or more virtual bandwidth), one can sacrifice
some of the gained bandwidth for FEC and therefore higher spectral
efficiency can also translate to higher quality.
[0088] Telecom operators and vendors are interested in increasing spectral
efficiency. However, the issue with respect to this increase is the cost.
Each technique at different layers of the protocol has a different price
tag associated therewith. Techniques that are implemented at a physical
layer have the most impact as other techniques can be superimposed on top
of the lower layer techniques and thus increase the spectral efficiency
further. The price tag for some of the techniques can be drastic when one
considers other associated costs. For example, the multiple input
multiple output (MIMO) technique uses additional antennas to create
additional paths where each RF path can be treated as an independent
channel and thus increase the aggregate spectral efficiency. In the MIMO
scenario, the operator has other associated soft costs dealing with
structural issues such as antenna installations, etc. These techniques
not only have tremendous cost, but they have huge timing issues as the
structural activities take time and the achieving of higher spectral
efficiency comes with significant delays which can also be translated to
financial losses.
[0089] The quantum level overlay technique 202 has an advantage that the
independent channels are created within the symbols without needing new
antennas. This will have a tremendous cost and time benefit compared to
other techniques. Also, the quantum layer overlay technique 202 is a
physical layer technique, which means there are other techniques at
higher layers of the protocol that can all ride on top of the QLO
techniques 202 and thus increase the spectral efficiency even further.
QLO technique 202 uses standard QAM modulation used in OFDM based
multiple access technologies such as WIMAX or LTE. QLO technique 202
basically enhances the QAM modulation at the transceiver by injecting new
signals to the I & Q components of the baseband and overlaying them
before QAM modulation as will be more fully described herein below. At
the receiver, the reverse procedure is used to separate the overlaid
signal and the net effect is a pulse shaping that allows better
localization of the spectrum compared to standard QAM or even the root
raised cosine. The impact of this technique is a significantly higher
spectral efficiency.
[0090] Referring now more particularly to FIG. 3, there is illustrated a
general overview of the manner for providing improved communication
bandwidth within various communication protocol interfaces 302, using a
combination of multiple level overlay modulation 304 and the application
of orbital angular momentum 306 to increase the number of communications
channels.
[0091] The various communication protocol interfaces 302 may comprise a
variety of communication links, such as RF communication, wireline
communication such as cable or twisted pair connections, or optical
communications making use of light wavelengths such as fiberoptic
communications or freespace optics. Various types of RF communications
may include a combination of RF microwave or RF satellite communication,
as well as multiplexing between RF and freespace optics in real time.
[0092] By combining a multiple layer overlay modulation technique 304 with
orbital angular momentum (OAM) technique 306, a higher throughput over
various types of communication links 302 may be achieved. The use of
multiple level overlay modulation alone without OAM increases the
spectral efficiency of communication links 302, whether wired, optical,
or wireless. However, with OAM, the increase in spectral efficiency is
even more significant.
[0093] Multiple overlay modulation techniques 304 provide a new degree of
freedom beyond the conventional 2 degrees of freedom, with time T and
frequency F being independent variables in a twodimensional notational
space defining orthogonal axes in an information diagram. This comprises
a more general approach rather than modeling signals as fixed in either
the frequency or time domain. Previous modeling methods using fixed time
or fixed frequency are considered to be more limiting cases of the
general approach of using multiple level overlay modulation 304. Within
the multiple level overlay modulation technique 304, signals may be
differentiated in twodimensional space rather than along a single axis.
Thus, the informationcarrying capacity of a communications channel may
be determined by a number of signals which occupy different time and
frequency coordinates and may be differentiated in a notational
twodimensional space.
[0094] Within the notational twodimensional space, minimization of the
time bandwidth product, i.e., the area occupied by a signal in that
space, enables denser packing, and thus, the use of more signals, with
higher resulting informationcarrying capacity, within an allocated
channel. Given the frequency channel delta (.DELTA.f), a given signal
transmitted through it in minimum time .DELTA.t will have an envelope
described by certain timebandwidth minimizing signals. The
timebandwidth products for these signals take the form;
.DELTA.t.DELTA.f=1/2(2n+1)
where n is an integer ranging from 0 to infinity, denoting the order of
the signal.
[0095] These signals form an orthogonal set of infinite elements, where
each has a finite amount of energy. They are finite in both the time
domain and the frequency domain, and can be detected from a mix of other
signals and noise through correlation, for example, by match filtering.
Unlike other wavelets, these orthogonal signals have similar time and
frequency forms.
[0096] The orbital angular momentum process 306 provides a twist to wave
fronts of the electromagnetic fields carrying the data stream that may
enable the transmission of multiple data streams on the same frequency,
wavelength, or other signalsupporting mechanism. This will increase the
bandwidth over a communications link by allowing a single frequency or
wavelength to support multiple eigen channels, each of the individual
channels having a different orthogonal and independent orbital angular
momentum associated therewith.
[0097] Referring now to FIG. 4, there is illustrated a further
communication implementation technique using the above described
techniques as twisted pairs or cables carry electrons (not photons).
Rather than using each of the multiple level overlay modulation 304 and
orbital angular momentum techniques 306, only the multiple level overlay
modulation 304 can be used in conjunction with a single wireline
interface and, more particularly, a twisted pair communication link or a
cable communication link 402. The operation of the multiple level overlay
modulation 404, is similar to that discussed previously with respect to
FIG. 3, but is used by itself without the use of orbital angular momentum
techniques 306, and is used with either a twisted pair communication link
or cable interface communication link 402.
[0098] Referring now to FIG. 5, there is illustrated a general block
diagram for processing a plurality of data streams 502 for transmission
in an optical communication system. The multiple data streams 502 are
provided to the multilayer overlay modulation circuitry 504 wherein the
signals are modulated using the multilayer overlay modulation technique.
The modulated signals are provided to orbital angular momentum processing
circuitry 506 which applies a twist to each of the wave fronts being
transmitted on the wavelengths of the optical communication channel. The
twisted waves are transmitted through the optical interface 508 over an
optical communications link such as an optical fiber or free space optics
communication system. FIG. 5 may also illustrate an RF mechanism wherein
the interface 508 would comprise and RF interface rather than an optical
interface.
[0099] Referring now more particularly to FIG. 6, there is illustrated a
functional block diagram of a system for generating the orbital angular
momentum "twist" within a communication system, such as that illustrated
with respect to FIG. 3, to provide a data stream that may be combined
with multiple other data streams for transmission upon a same wavelength
or frequency. Multiple data streams 602 are provided to the transmission
processing circuitry 600. Each of the data streams 602 comprises, for
example, an end to end link connection carrying a voice call or a packet
connection transmitting noncircuit switch packed data over a data
connection. The multiple data streams 602 are processed by
modulator/demodulator circuitry 604. The modulator/demodulator circuitry
604 modulates the received data stream 602 onto a wavelength or frequency
channel using a multiple level overlay modulation technique, as will be
more fully described herein below. The communications link may comprise
an optical fiber link, freespace optics link, RF microwave link, RF
satellite link, wired link (without the twist), etc.
[0100] The modulated data stream is provided to the orbital angular
momentum (OAM) signal processing block 606. Each of the modulated data
streams from the modulator/demodulator 604 are provided a different
orbital angular momentum by the orbital angular momentum electromagnetic
block 606 such that each of the modulated data streams have a unique and
different orbital angular momentum associated therewith. Each of the
modulated signals having an associated orbital angular momentum are
provided to an optical transmitter 608 that transmits each of the
modulated data streams having a unique orbital angular momentum on a same
wavelength. Each wavelength has a selected number of bandwidth slots B
and may have its data transmission capability increase by a factor of the
number of degrees of orbital angular momentum l that are provided from
the OAM electromagnetic block 606. The optical transmitter 608
transmitting signals at a single wavelength could transmit B groups of
information. The optical transmitter 608 and OAM electromagnetic block
606 may transmit l.times.B groups of information according to the
configuration described herein.
[0101] In a receiving mode, the optical transmitter 608 will have a
wavelength including multiple signals transmitted therein having
different orbital angular momentum signals embedded therein. The optical
transmitter 608 forwards these signals to the OAM signal processing block
606, which separates each of the signals having different orbital angular
momentum and provides the separated signals to the demodulator circuitry
604. The demodulation process extracts the data streams 602 from the
modulated signals and provides it at the receiving end using the multiple
layer overlay demodulation technique.
[0102] Referring now to FIG. 7, there is provided a more detailed
functional description of the OAM signal processing block 606. Each of
the input data streams are provided to OAM circuitry 702. Each of the OAM
circuitry 702 provides a different orbital angular momentum to the
received data stream. The different orbital angular momentums are
achieved by applying different currents for the generation of the signals
that are being transmitted to create a particular orbital angular
momentum associated therewith. The orbital angular momentum provided by
each of the OAM circuitries 702 are unique to the data stream that is
provided thereto. An infinite number of orbital angular momentums may be
applied to different input data streams using many different currents.
Each of the separately generated data streams are provided to a signal
combiner 704, which combines the signals onto a wavelength for
transmission from the transmitter 706.
[0103] Referring now to FIG. 8, there is illustrated the manner in which
the OAM processing circuitry 606 may separate a received signal into
multiple data streams. The receiver 802 receives the combined OAM signals
on a single wavelength and provides this information to a signal
separator 804. The signal separator 804 separates each of the signals
having different orbital angular momentums from the received wavelength
and provides the separated signals to OAM detwisting circuitry 806. The
OAM detwisting circuitry 806 removes the associated OAM twist from each
of the associated signals and provides the received modulated data stream
for further processing. The signal separator 804 separates each of the
received signals that have had the orbital angular momentum removed
therefrom into individual received signals. The individually received
signals are provided to the receiver 802 for demodulation using, for
example, multiple level overlay demodulation as will be more fully
described herein below.
[0104] FIG. 9 illustrates in a manner in which a single wavelength or
frequency, having two quantispin polarizations may provide an infinite
number of twists having various orbital angular momentums associated
therewith. The l axis represents the various quantized orbital angular
momentum states which may be applied to a particular signal at a selected
frequency or wavelength. The symbol omega (.omega.) represents the
various frequencies to which the signals of differing orbital angular
momentum may be applied. The top grid 902 represents the potentially
available signals for a left handed signal polarization, while the bottom
grid 904 is for potentially available signals having right handed
polarization.
[0105] By applying different orbital angular momentum states to a signal
at a particular frequency or wavelength, a potentially infinite number of
states may be provided at the frequency or wavelength. Thus, the state at
the frequency .DELTA..omega. or wavelength 906 in both the left handed
polarization plane 902 and the right handed polarization plane 904 can
provide an infinite number of signals at different orbital angular
momentum states .DELTA.l. Blocks 908 and 910 represent a particular
signal having an orbital angular momentum .DELTA.l at a frequency
.DELTA..omega. or wavelength in both the right handed polarization plane
904 and left handed polarization plane 910, respectively. By changing to
a different orbital angular momentum within the same frequency
.DELTA..omega. or wavelength 906, different signals may also be
transmitted. Each angular momentum state corresponds to a different
determined current level for transmission from the optical transmitter.
By estimating the equivalent current for generating a particular orbital
angular momentum within the optical domain and applying this current for
transmission of the signals, the transmission of the signal may be
achieved at a desired orbital angular momentum state.
[0106] Thus, the illustration of FIG. 9, illustrates two possible angular
momentums, the spin angular momentum, and the orbital angular momentum.
The spin version is manifested within the polarizations of macroscopic
electromagnetism, and has only left and right hand polarizations due to
up and down spin directions. However, the orbital angular momentum
indicates an infinite number of states that are quantized. The paths are
more than two and can theoretically be infinite through the quantized
orbital angular momentum levels.
[0107] Using the orbital angular momentum state of the transmitted energy
signals, physical information can be embedded within the radiation
transmitted by the signals. The MaxwellHeaviside equations can be
represented as:
.gradient. E = .rho. 0 ##EQU00001## .gradient. .times. E
=  .differential. B .differential. t ##EQU00001.2##
.gradient. B = 0 ##EQU00001.3## .gradient. .times. B = 0
.mu. 0 .differential. E .differential. t + .mu. 0 j
( t , x ) ##EQU00001.4##
where .gradient. is the del operator, E is the electric field intensity
and B is the magnetic flux density. Using these equations, one can derive
23 symmetries/conserved quantities from Maxwell's original equations.
However, there are only ten wellknown conserved quantities and only a
few of these are commercially used. Historically if Maxwell's equations
where kept in their original quaternion forms, it would have been easier
to see the symmetries/conserved quantities, but when they were modified
to their present vectorial form by Heaviside, it became more difficult to
see such inherent symmetries in Maxwell's equations.
[0108] Maxwell's linear theory is of U(1) symmetry with Abelian
commutation relations. They can be extended to higher symmetry group
SU(2) form with nonAbelian commutation relations that address global
(nonlocal in space) properties. The WuYang and Harmuth interpretation
of Maxwell's theory implicates the existence of magnetic monopoles and
magnetic charges. As far as the classical fields are concerned, these
theoretical constructs are pseudoparticle, or instanton. The
interpretation of Maxwell's work actually departs in a significant ways
from Maxwell's original intention. In Maxwell's original formulation,
Faraday's electrotonic states (the A.mu. field) was central making them
compatible with YangMills theory (prior to Heaviside). The mathematical
dynamic entities called solitons can be either classical or quantum,
linear or nonlinear and describe EM waves. However, solitons are of
SU(2) symmetry forms. In order for conventional interpreted classical
Maxwell's theory of U(1) symmetry to describe such entities, the theory
must be extended to SU(2) forms.
[0109] Besides the half dozen physical phenomena (that cannot be explained
with conventional Maxwell's theory), the recently formulated Harmuth
Ansatz also address the incompleteness of Maxwell's theory. Harmuth
amended Maxwell's equations can be used to calculate EM signal velocities
provided that a magnetic current density and magnetic charge are added
which is consistent to YangMills filed equations. Therefore, with the
correct geometry and topology, the A.mu. potentials always have physical
meaning
[0110] The conserved quantities and the electromagnetic field can be
represented according to the conservation of system energy and the
conservation of system linear momentum. Time symmetry, i.e. the
conservation of system energy can be represented using Poynting's theorem
according to the equations:
H = i m i .gamma. i c 2 + 0 2 .intg. d
3 x ( E 2 + c 2 B 2 ) Hamiltonian
( total energy ) dU mech dt + dU em dt +
s ' d 2 x ' n ' ^ S = 0 conservation
of energy ##EQU00002##
[0111] The space symmetry, i.e., the conservation of system linear
momentum representing the electromagnetic Doppler shift can be
represented by the equations:
p = i m i .gamma. i v i + 0 .intg. d 3
x ( E .times. B ) linear momentum dp
mech dt + dp em dt + s ' d 2 x ' n ' ^ T
= 0 conservation of linear momentum
##EQU00003##
[0112] The conservation of system center of energy is represented by the
equation:
R = 1 H i ( x i  x 0 ) m i .gamma. i c
2 + 0 2 H .intg. d 3 x ( x  x 0 ) (
E 2 + c 2 B 2 ) ##EQU00004##
Similarly, the conservation of system angular momentum, which gives rise
to the azimuthal Doppler shift is represented by the equation:
dJ mech dt + dJ em dt + s ' d 2 x ' n '
^ M = 0 conservation of angular momentum
##EQU00005##
[0113] For radiation beams in free space, the EM field angular momentum
J.sup.em can be separated into two parts:
J.sup.em=.epsilon..sub.0.intg..sub.V'd.sup.3x'(E.times.A)+.epsilon..sub.
0.intg..sub.V'd.sup.3x'E.sub.i[(x'x.sub.0).times..gradient.]A.sub.i
[0114] For each singular Fourier mode in real valued representation:
J em =  i 0 2 .omega. .intg. V ' d 3 x
' ( E * .times. E )  i 0 2 .omega. .intg.
V ' d 3 x ' E i [ ( x '  x 0 ) .times.
.gradient. ] E i ##EQU00006##
[0115] The first part is the EM spin angular momentum S.sup.em, its
classical manifestation is wave polarization. And the second part is the
EM orbital angular momentum L.sup.em its classical manifestation is wave
helicity. In general, both EM linear momentum P.sup.em, and EM angular
momentum J.sup.em=L.sup.em+S.sup.em are radiated all the way to the far
field.
[0116] By using Poynting theorem, the optical vorticity of the signals may
be determined according to the optical velocity equation:
.differential. U .differential. t + .gradient. S = 0 ,
continuity equation ##EQU00007##
where S is the Poynting vector
S=1/4(E.times.H*+E*.times.H),
and U is the energy density
U=1/4(.epsilon.E.sup.2+.mu..sub.0H.sup.2),
with E and H comprising the electric field and the magnetic field,
respectively, and .epsilon. and .mu..sub.0 being the permittivity and the
permeability of the medium, respectively. The optical vorticity V may
then be determined by the curl of the optical velocity according to the
equation:
V = .gradient. .times. v opt = .gradient. .times. ( E
.times. H * + E * .times. H E 2 + .mu. 0 H
2 ) ##EQU00008##
[0117] Referring now to FIGS. 10A and 10B, there is illustrated the manner
in which a signal and its associated Poynting vector in a plane wave
situation. In the plane wave situation illustrated generally at 1002, the
transmitted signal may take one of three configurations. When the
electric field vectors are in the same direction, a linear signal is
provided, as illustrated generally at 1004. Within a circular
polarization 1006, the electric field vectors rotate with the same
magnitude. Within the elliptical polarization 1008, the electric field
vectors rotate but have differing magnitudes. The Poynting vector remains
in a constant direction for the signal configuration to FIG. 10A and
always perpendicular to the electric and magnetic fields. Referring now
to FIG. 10B, when a unique orbital angular momentum is applied to a
signal as described here and above, the Poynting vector S 1010 will
spiral about the direction of propagation of the signal. This spiral may
be varied in order to enable signals to be transmitted on the same
frequency as described herein.
[0118] FIGS. 11A through 11C illustrate the differences in signals having
different helicity (i.e., orbital angular momentums). Each of the
spiraling Poynting vectors associated with the signals 1102, 1104, and
1106 provide a different shaped signal. Signal 1102 has an orbital
angular momentum of +1, signal 1104 has an orbital angular momentum of
+3, and signal 1106 has an orbital angular momentum of 4. Each signal
has a distinct angular momentum and associated Poynting vector enabling
the signal to be distinguished from other signals within a same
frequency. This allows differing type of information to be transmitted on
the same frequency, since these signals are separately detectable and do
not interfere with each other (Eigen channels).
[0119] FIG. 11D illustrates the propagation of Poynting vectors for
various Eigen modes. Each of the rings 1120 represents a different Eigen
mode or twist representing a different orbital angular momentum within
the same frequency. Each of these rings 1120 represents a different
orthogonal channel. Each of the Eigen modes has a Poynting vector 1122
associated therewith.
[0120] Topological charge may be multiplexed to the frequency for either
linear or circular polarization. In case of linear polarizations,
topological charge would be multiplexed on vertical and horizontal
polarization. In case of circular polarization, topological charge would
multiplex on left hand and right hand circular polarizations. The
topological charge is another name for the helicity index "I" or the
amount of twist or OAM applied to the signal. The helicity index may be
positive or negative. In RF, different topological charges can be created
and muxed together and demuxed to separate the topological charges.
[0121] The topological charges l s can be created using Spiral Phase
Plates (SPPs) as shown in FIG. 11E using a proper material with specific
index of refraction and ability to machine shop or phase mask, holograms
created of new materials or a new technique to create an RF version of
Spatial Light Modulator (SLM) that does the twist of the RF waves (as
opposed to optical beams) by adjusting voltages on the device resulting
in twisting of the RF waves with a specific topological charge. Spiral
Phase plates can transform a RF plane wave (l=0) to a twisted RF wave of
a specific helicity (i.e. l=+1).
[0122] Cross talk and multipath interference can be corrected using RF
MultipleInputMultipleOutput (MIMO). Most of the channel impairments
can be detected using a control or pilot channel and be corrected using
algorithmic techniques (closed loop control system).
[0123] As described previously with respect to FIG. 5, each of the
multiple data streams applied within the processing circuitry has a
multiple layer overlay modulation scheme applied thereto.
[0124] Referring now to FIG. 12, the reference number 1200 generally
indicates an embodiment of a multiple level overlay (MLO) modulation
system, although it should be understood that the term MLO and the
illustrated system 1200 are examples of embodiments. The MLO system may
comprise one such as that disclosed in U.S. Pat. No. 8,503,546 entitled
Multiple Layer Overlay Modulation which is incorporated herein by
reference. In one example, the modulation system 1200 would be
implemented within the multiple level overlay modulation box 504 of FIG.
5. System 1200 takes as input an input data stream 1201 from a digital
source 1202, which is separated into three parallel, separate data
streams, 1203A1203C, of logical 1s and 0s by input stage demultiplexer
(DEMUX) 1004. Data stream 1001 may represent a data file to be
transferred, or an audio or video data stream. It should be understood
that a greater or lesser number of separated data streams may be used. In
some of the embodiments, each of the separated data streams 1203A1203C
has a data rate of 1/N of the original rate, where N is the number of
parallel data streams. In the embodiment illustrated in FIG. 12, N is 3.
[0125] Each of the separated data streams 1203A1203C is mapped to a
quadrature amplitude modulation (QAM) symbol in an MQAM constellation,
for example, 16 QAM or 64 QAM, by one of the QAM symbol mappers 1205AC.
The QAM symbol mappers 1205AC are coupled to respective outputs of DEMUX
1204, and produced parallel in phase (I) 1206A, 1208A, and 1210A and
quadrature phase (Q) 1206B, 1208B, and 1210B data streams at discrete
levels. For example, in 64 QAM, each I and Q channel uses 8 discrete
levels to transmit 3 bits per symbol. Each of the three I and Q pairs,
1206A1206B, 1208A1208B, and 1210A1210B, is used to weight the output
of the corresponding pair of function generators 1207A1207B,
1209A1209B, and 1211A1211B, which in some embodiments generate signals
such as the modified Hermite polynomials described above and weights them
based on the amplitude value of the input symbols. This provides 2N
weighted or modulated signals, each carrying a portion of the data
originally from income data stream 1201, and is in place of modulating
each symbol in the I and Q pairs, 1206A1206B, 1208A1208B, and
1210A1210B with a raised cosine filter, as would be done for a prior art
QAM system. In the illustrated embodiment, three signals are used, SH0,
SH1, and SH2, which correspond to modifications of H0, H1, and H2,
respectively, although it should be understood that different signals may
be used in other embodiments.
[0126] The weighted signals are not subcarriers, but rather are sublayers
of a modulated carrier, and are combined, superimposed in both frequency
and time, using summers 1212 and 1216, without mutual interference in
each of the I and Q dimensions, due to the signal orthogonality. Summers
1212 and 1216 act as signal combiners to produce composite signals 1213
and 1217. The weighted orthogonal signals are used for both I and Q
channels, which have been processed equivalently by system 1200, and are
summed before the QAM signal is transmitted. Therefore, although new
orthogonal functions are used, some embodiments additionally use QAM for
transmission. Because of the tapering of the signals in the time domain,
as will be shown in FIGS. 16A through 16K, the time domain waveform of
the weighted signals will be confined to the duration of the symbols.
Further, because of the tapering of the special signals and frequency
domain, the signal will also be confined to frequency domain, minimizing
interface with signals and adjacent channels.
[0127] The composite signals 1213 and 1217 are converted to analogue
signals 1215 and 1219 using digital to analogue converters 1214 and 1218,
and are then used to modulate a carrier signal at the frequency of local
oscillator (LO) 1220, using modulator 1221. Modulator 1221 comprises
mixers 1222 and 1224 coupled to DACs 1214 and 1218, respectively. Ninety
degree phase shifter 1223 converts the signals from LO 1220 into a Q
component of the carrier signal. The output of mixers 1222 and 1224 are
summed in summer 1225 to produce output signals 1226.
[0128] MLO can be used with a variety of transport mediums, such as wire,
optical, and wireless, and may be used in conjunction with QAM. This is
because MLO uses spectral overlay of various signals, rather than
spectral overlap. Bandwidth utilization efficiency may be increased by an
order of magnitude, through extensions of available spectral resources
into multiple layers. The number of orthogonal signals is increased from
2, cosine and sine, in the prior art, to a number limited by the accuracy
and jitter limits of generators used to produce the orthogonal
polynomials. In this manner, MLO extends each of the I and Q dimensions
of QAM to any multiple access techniques such as GSM, code division
multiple access (CDMA), wide band CDMA (WCDMA), high speed downlink
packet access (HSPDA), evolutiondata optimized (EVDO), orthogonal
frequency division multiplexing (OFDM), worldwide interoperability for
microwave access (WIMAX), and long term evolution (LTE) systems. MLO may
be further used in conjunction with other multiple access (MA) schemes
such as frequency division duplexing (FDD), time division duplexing
(TDD), frequency division multiple access (FDMA), and time division
multiple access (TDMA). Overlaying individual orthogonal signals over the
same frequency band allows creation of a virtual bandwidth wider than the
physical bandwidth, thus adding a new dimension to signal processing.
This modulation is applicable to twisted pair, cable, fiber optic,
satellite, broadcast, freespace optics, and all types of wireless
access. The method and system are compatible with many current and future
multiple access systems, including EVDO, UMB, WIMAX, WCDMA (with or
without), multimedia broadcast multicast service (MBMS)/multiple input
multiple output (MIMO), HSPA evolution, and LTE.
[0129] Referring now to FIG. 13, an MLO demodulator 1300 is illustrated,
although it should be understood that the term MLO and the illustrated
system 1300 are examples of embodiments. The modulator 1300 takes as
input an MLO signal 1126 which may be similar to output signal 1226 from
system 1200. Synchronizer 1327 extracts phase information, which is input
to local oscillator 1320 to maintain coherence so that the modulator 1321
can produce base band to analogue I signal 1315 and Q signal 1319. The
modulator 1321 comprises mixers 1322 and 1324, which, coupled to OL1320
through 90 degree phase shifter 1323. I signal 1315 is input to each of
signal filters 1307A, 1309A, and 1311A, and Q signal 1319 is input to
each of signal filters 1307B, 1309B, and 1311B. Since the orthogonal
functions are known, they can be separated using correlation or other
techniques to recover the modulated data. Information in each of the I
and Q signals 1315 and 1319 can be extracted from the overlapped
functions which have been summed within each of the symbols because the
functions are orthogonal in a correlative sense.
[0130] In some embodiments, signal filters 1307A1307B, 1309A1309B, and
1311A1311B use locally generated replicas of the polynomials as known
signals in match filters. The outputs of the match filters are the
recovered data bits, for example, equivalence of the QAM symbols
1306A1306B, 1308A1308B, and 1310A1310B of system 1300. Signal filters
1307A1307B, 1309A1309B, and 1311A1311B produce 2n streams of n, I, and
Q signal pairs, which are input into demodulators 13281333. Demodulators
13281333 integrate the energy in their respective input signals to
determine the value of the QAM symbol, and hence the logical 1s and 0s
data bit stream segment represented by the determined symbol. The outputs
of the modulators 13281333 are then input into multiplexers (MUXs)
1305A1305C to generate data streams 1303A1303C. If system 1300 is
demodulating a signal from system 1200, data streams 1303A1303C
correspond to data streams 1203A1203C. Data streams 1303A1303C are
multiplexed by MUX 1304 to generate data output stream 1301. In summary,
MLO signals are overlayed (stacked) on top of one another on transmitter
and separated on receiver.
[0131] MLO may be differentiated from CDMA or OFDM by the manner in which
orthogonality among signals is achieved. MLO signals are mutually
orthogonal in both time and frequency domains, and can be overlaid in the
same symbol time bandwidth product. Orthogonality is attained by the
correlation properties, for example, by least sum of squares, of the
overlaid signals. In comparison, CDMA uses orthogonal interleaving or
displacement of signals in the time domain, whereas OFDM uses orthogonal
displacement of signals in the frequency domain.
[0132] Bandwidth efficiency may be increased for a channel by assigning
the same channel to multiple users. This is feasible if individual user
information is mapped to special orthogonal functions. CDMA systems
overlap multiple user information and views time intersymbol orthogonal
code sequences to distinguish individual users, and OFDM assigns unique
signals to each user, but which are not overlaid, are only orthogonal in
the frequency domain. Neither CDMA nor OFDM increases bandwidth
efficiency. CDMA uses more bandwidth than is necessary to transmit data
when the signal has a low signal to noise ratio (SNR). OFDM spreads data
over many subcarriers to achieve superior performance in multipath
radiofrequency environments. OFDM uses a cyclic prefix OFDM to mitigate
multipath effects and a guard time to minimize intersymbol interference
(ISI), and each channel is mechanistically made to behave as if the
transmitted waveform is orthogonal. (Sync function for each subcarrier in
frequency domain.)
[0133] In contrast, MLO uses a set of functions which effectively form an
alphabet that provides more usable channels in the same bandwidth,
thereby enabling high bandwidth efficiency. Some embodiments of MLO do
not require the use of cyclic prefixes or guard times, and therefore,
outperforms OFDM in spectral efficiency, peak to average power ratio,
power consumption, and requires fewer operations per bit. In addition,
embodiments of MLO are more tolerant of amplifier nonlinearities than are
CDMA and OFDM systems.
[0134] FIG. 14 illustrates an embodiment of an MLO transmitter system
1400, which receives input data stream 1401. System 1400 represents a
modulator/controller 1401, which incorporates equivalent functionality of
DEMUX 1204, QAM symbol mappers 1205AC, function generators 1207A1207B,
1209A1209B, and 1211A1211B, and summers 1212 and 1216 of system 1200,
shown in FIG. 12. However, it should be understood that
modulator/controller 1401 may use a greater or lesser quantity of signals
than the three illustrated in system 1200. Modulator/controller 1401 may
comprise an application specific integrated circuit (ASIC), a field
programmable gate array (FPGA), and/or other components, whether discrete
circuit elements or integrated into a single integrated circuit (IC)
chip.
[0135] Modulator/controller 1401 is coupled to DACs 1404 and 1407,
communicating a 10 bit I signal 1402 and a 10 bit Q signal 1405,
respectively. In some embodiments, I signal 1402 and Q signal 1405
correspond to composite signals 1213 and 1217 of system 1200. It should
be understood, however, that the 10 bit capacity of I signal 1402 and Q
signal 1405 is merely representative of an embodiment. As illustrated,
modulator/controller 1401 also controls DACs 1404 and 1407 using control
signals 1403 and 1406, respectively. In some embodiments, DACs 1404 and
1407 each comprise an AD5433, complementary metal oxide semiconductor
(CMOS) 10 bit current output DAC. In some embodiments, multiple control
signals are sent to each of DACs 1404 and 1407.
[0136] DACs 1404 and 1407 output analogue signals 1215 and 1219 to
quadrature modulator 1221, which is coupled to LO 1220. The output of
modulator 1220 is illustrated as coupled to a transmitter 1408 to
transmit data wirelessly, although in some embodiments, modulator 1221
may be coupled to a fiberoptic modem, a twisted pair, a coaxial cable,
or other suitable transmission media.
[0137] FIG. 15 illustrates an embodiment of an MLO receiver system 1500
capable of receiving and demodulating signals from system 1400. System
1500 receives an input signal from a receiver 1508 that may comprise
input medium, such as RF, wired or optical. The modulator 1321 driven by
LO 1320 converts the input to baseband I signal 1315 and Q signal 1319. I
signal 1315 and Q signal 1319 are input to analogue to digital converter
(ADC) 1509.
[0138] ADC 1509 outputs 10 bit signal 1510 to demodulator/controller 1501
and receives a control signal 1512 from demodulator/controller 1501.
Demodulator/controller 1501 may comprise an application specific
integrated circuit (ASIC), a field programmable gate array (FPGA), and/or
other components, whether discrete circuit elements or integrated into a
single integrated circuit (IC) chip. Demodulator/controller 1501
correlates received signals with locally generated replicas of the signal
set used, in order to perform demodulation and identify the symbols sent.
Demodulator/controller 1501 also estimates frequency errors and recovers
the data clock, which is used to read data from the ADC 1509. The clock
timing is sent back to ADC 1509 using control signal 1512, enabling ADC
1509 to segment the digital I and Q signals 1315 and 1319. In some
embodiments, multiple control signals are sent by demodulator/controller
1501 to ADC 1509. Demodulator/controller 1501 also outputs data signal
1301.
[0139] Hermite polynomials are a classical orthogonal polynomial sequence,
which are the Eigenstates of a quantum harmonic oscillator. Signals based
on Hermite polynomials possess the minimal timebandwidth product
property described above, and may be used for embodiments of MLO systems.
However, it should be understood that other signals may also be used, for
example orthogonal polynomials such as Jacobi polynomials, Gegenbauer
polynomials, Legendre polynomials, Chebyshev polynomials, and Laguerre
polynomials. Qfunctions are another class of functions that can be
employed as a basis for MLO signals.
[0140] In quantum mechanics, a coherent state is a state of a quantum
harmonic oscillator whose dynamics most closely resemble the oscillating
behavior of a classical harmonic oscillator system. A squeezed coherent
state is any state of the quantum mechanical Hilbert space, such that the
uncertainty principle is saturated. That is, the product of the
corresponding two operators takes on its minimum value. In embodiments of
an MLO system, operators correspond to time and frequency domains wherein
the timebandwidth product of the signals is minimized. The squeezing
property of the signals allows scaling in time and frequency domain
simultaneously, without losing mutual orthogonality among the signals in
each layer. This property enables flexible implementations of MLO systems
in various communications systems.
[0141] Because signals with different orders are mutually orthogonal, they
can be overlaid to increase the spectral efficiency of a communication
channel. For example, when n=0, the optimal baseband signal will have a
timebandwidth product of 1/2, which is the Nyquist InterSymbol
Interference (ISI) criteria for avoiding ISI. However, signals with
timebandwidth products of 3/2, 5/2, 7/2, and higher, can be overlaid to
increase spectral efficiency.
[0142] An embodiment of an MLO system uses functions based on modified
Hermite polynomials, 4n, and are defined by:
.psi. n ( t , .xi. ) = ( tanh .xi. ) n / 2
2 n / 2 ( n ! cosh .xi. ) 1 / 2 e 1 2
t 2 [ 1  tan h .xi. ] H n ( t 2 cosh
.xi.sinh .xi. ) ##EQU00009##
where t is time, and .xi. is a bandwidth utilization parameter. Plots of
.PSI..sub.n for n ranging from 0 to 9, along with their Fourier
transforms (amplitude squared), are shown in FIGS. 5A5K. The
orthogonality of different orders of the functions may be verified by
integrating:
.intg..intg..psi..sub.n(t,.xi.).psi..sub.m(t,.xi.)dtd.xi.
[0143] The Hermite polynomial is defined by the contour integral:
H n ( z ) = n ! 2 .pi. i e  t 2 +
2 t2 t  n  1 dt , ##EQU00010##
where the contour encloses the origin and is traversed in a
counterclockwise direction. Hermite polynomials are described in
Mathematical Methods for Physicists, by George Arfken, for example on
page 416, the disclosure of which is incorporated by reference.
[0144] FIGS. 16A16K illustrate representative MLO signals and their
respective spectral power densities based on the modified Hermite
polynomials .PSI..sub.n for n ranging from 0 to 9. FIG. 16A shows plots
1601 and 1604. Plot 1601 comprises a curve 1627 representing .PSI..sub.0
plotted against a time axis 1602 and an amplitude axis 1603. As can be
seen in plot 1601, curve 1627 approximates a Gaussian curve. Plot 1604
comprises a curve 1637 representing the power spectrum of .PSI..sub.0
plotted against a frequency axis 1605 and a power axis 1606. As can be
seen in plot 1604, curve 1637 also approximates a Gaussian curve.
Frequency domain curve 1607 is generated using a Fourier transform of
time domain curve 1627. The units of time and frequency on axis 1602 and
1605 are normalized for baseband analysis, although it should be
understood that since the time and frequency units are related by the
Fourier transform, a desired time or frequency span in one domain
dictates the units of the corresponding curve in the other domain. For
example, various embodiments of MLO systems may communicate using symbol
rates in the megahertz (MHz) or gigahertz (GHz) ranges and the non0
duration of a symbol represented by curve 1627, i.e., the time period at
which curve 1627 is above 0 would be compressed to the appropriate length
calculated using the inverse of the desired symbol rate. For an available
bandwidth in the megahertz range, the non0 duration of a time domain
signal will be in the microsecond range.
[0145] FIGS. 16B16J show plots 16071624, with time domain curves
16281636 representing .PSI..sub.1 through .PSI..sub.9, respectively, and
their corresponding frequency domain curves 16381646. As can be seen in
FIGS. 16A16J, the number of peaks in the time domain plots, whether
positive or negative, corresponds to the number of peaks in the
corresponding frequency domain plot. For example, in plot 1623 of FIG.
16J, time domain curve 1636 has five positive and five negative peaks. In
corresponding plot 1624 therefore, frequency domain curve 1646 has ten
peaks.
[0146] FIG. 16K shows overlay plots 1625 and 1626, which overlay curves
16271636 and 16371646, respectively. As indicated in plot 1625, the
various time domain curves have different durations. However, in some
embodiments, the nonzero durations of the time domain curves are of
similar lengths. For an MLO system, the number of signals used represents
the number of overlays and the improvement in spectral efficiency. It
should be understood that, while ten signals are disclosed in FIGS.
16A16K, a greater or lesser quantity of signals may be used, and that
further, a different set of signals, rather than the .PSI..sub.n signals
plotted, may be used.
[0147] MLO signals used in a modulation layer have minimum timebandwidth
products, which enable improvements in spectral efficiency, and are
quadratically integrable. This is accomplished by overlaying multiple
demultiplexed parallel data streams, transmitting them simultaneously
within the same bandwidth. The key to successful separation of the
overlaid data streams at the receiver is that the signals used within
each symbols period are mutually orthogonal. MLO overlays orthogonal
signals within a single symbol period. This orthogonality prevents ISI
and intercarrier interference (ICI).
[0148] Because MLO works in the baseband layer of signal processing, and
some embodiments use QAM architecture, conventional wireless techniques
for optimizing air interface, or wireless segments, to other layers of
the protocol stack will also work with MLO. Techniques such as channel
diversity, equalization, error correction coding, spread spectrum,
interleaving and spacetime encoding are applicable to MLO. For example,
time diversity using a multipathmitigating rake receiver can also be
used with MLO. MLO provides an alternative for higher order QAM, when
channel conditions are only suitable for low order QAM, such as in fading
channels. MLO can also be used with CDMA to extend the number of
orthogonal channels by overcoming the Walsh code limitation of CDMA. MLO
can also be applied to each tone in an OFDM signal to increase the
spectral efficiency of the OFDM systems.
[0149] Embodiments of MLO systems amplitude modulate a symbol envelope to
create subenvelopes, rather than subcarriers. For data encoding, each
subenvelope is independently modulated according to NQAM, resulting in
each subenvelope independently carrying information, unlike OFDM. Rather
than spreading information over many subcarriers, as is done in OFDM,
for MLO, each subenvelope of the carrier carries separate information.
This information can be recovered due to the orthogonality of the
subenvelopes defined with respect to the sum of squares over their
duration and/or spectrum. Pulse train synchronization or temporal code
synchronization, as needed for CDMA, is not an issue, because MLO is
transparent beyond the symbol level. MLO addresses modification of the
symbol, but since CDMA and TDMA are spreading techniques of multiple
symbol sequences over time. MLO can be used along with CDMA and TDMA.
[0150] FIG. 17 illustrates a comparison of MLO signal widths in the time
and frequency domains. Time domain envelope representations 17011703 of
signals SH0SH3 are illustrated as all having a duration T.sub.S. SH0SH3
may represent PSI.sub.0PSI.sub.2, or may be other signals. The
corresponding frequency domain envelope representations are 17051707,
respectively. SH0 has a bandwidth BW, SH1 has a bandwidth three times BW,
and SH2 has a bandwidth of 5BW, which is five times as great as that of
SH0. The bandwidth used by an MLO system will be determined, at least in
part, by the widest bandwidth of any of the signals used. If each layer
uses only a single signal type within identical time windows, the
spectrum will not be fully utilized, because the lower order signals will
use less of the available bandwidth than is used by the higher order
signals.
[0151] FIG. 18 illustrates a spectral alignment of MLO signals that
accounts for the differing bandwidths of the signals, and makes spectral
usage more uniform, using SH0SH3. Blocks 18011804 are frequency domain
blocks of an OFDM signal with multiple subcarriers. Block 1803 is
expanded to show further detail. Block 1803 comprises a first layer 1803x
comprised of multiple SH0 envelopes 1803a1803o. A second layer 1803y of
SH1 envelopes 1803p1803t has one third the number of envelopes as the
first layer. In the illustrated example, first layer 1803x has 15 SH0
envelopes, and second layer 1803y has five SH1 envelopes. This is
because, since the SH1 bandwidth envelope is three times as wide as that
of SH0, 15 SH0 envelopes occupy the same spectral width as five SH1
envelopes. The third layer 1803z of block 1803 comprises three SH2
envelopes 1803u1803w, because the SH2 envelope is five times the width
of the SH0 envelope.
[0152] The total required bandwidth for such an implementation is a
multiple of the least common multiple of the bandwidths of the MLO
signals. In the illustrated example, the least common multiple of the
bandwidth required for SH0, SH1, and SH2 is 15BW, which is a block in the
frequency domain. The OFDMMLO signal can have multiple blocks, and the
spectral efficiency of this illustrated implementation is proportional to
(15+5+3)/15.
[0153] FIG. 19 illustrates another spectral alignment of MLO signals,
which may be used alternatively to alignment scheme shown in FIG. 18. In
the embodiment illustrated in FIG. 19, the OFDMMLO implementation stacks
the spectrum of SH0, SH1, and SH2 in such a way that the spectrum in each
layer is utilized uniformly. Layer 1900A comprises envelopes 1901A1901D,
which includes both SH0 and SH2 envelopes. Similarly, layer 1900C,
comprising envelopes 1903A1903D, includes both SH0 and SH2 envelopes.
Layer 1900B, however, comprising envelopes 1902A1902D, includes only SH1
envelopes. Using the ratio of envelope sizes described above, it can be
easily seen that BW+5BW=3BW+3BW. Thus, for each SH0 envelope in layer
1900A, there is one SH2 envelope also in layer 1900C and two SH1
envelopes in layer 1900B.
Three Scenarios Compared:
[0154] 1) MLO with 3 Layers defined by:
f 0 ( t ) = W 0 e  t 2 4 , W 0 = 0.6316
##EQU00011## f 1 ( t ) = W 1 t e  t 2 4
, W 1 .apprxeq. 0.6316 ##EQU00011.2## f 2 ( t ) = W 2
( t 2  1 ) e  t 2 4 , W 2 .apprxeq. 0.4466
##EQU00011.3##
(The current FPGA implementation uses the truncation interval of [6,
6].) 2) Conventional scheme using rectangular pulse 3) Conventional
scheme using a squareroot raised cosine (SRRC) pulse with a rolloff
factor of 0.5
[0155] For MLO pulses and SRRC pulse, the truncation interval is denoted
by [t1, t1] in the following figures. For simplicity, we used the MLO
pulses defined above, which can be easily scaled in time to get the
desired time interval (say microseconds or nanoseconds). For the SRRC
pulse, we fix the truncation interval of [3T, 3T] where T is the symbol
duration for all results presented in this document.
Bandwidth Efficiency
[0156] The XdB bounded power spectral density bandwidth is defined as the
smallest frequency interval outside which the power spectral density
(PSD) is X dB below the maximum value of the PSD. The XdB can be
considered as the outofband attenuation.
[0157] The bandwidth efficiency is expressed in Symbols per second per
Hertz. The bit per second per Hertz can be obtained by multiplying the
symbols per second per Hertz with the number of bits per symbol (i.e.,
multiplying with log 2 M for Mary QAM).
[0158] Truncation of MLO pulses introduces interlayer interferences
(ILI). However, the truncation interval of [6, 6] yields negligible ILI
while [4, 4] causes slight tolerable ILI.
[0159] The bandwidth efficiency of MLO may be enhanced by allowing
intersymbol interference (ISI). To realize this enhancement, designing
transmitter side parameters as well as developing receiver side detection
algorithms and error performance evaluation can be performed.
[0160] Referring now to FIG. 20, there is illustrated the power spectral
density of each layer SH0SH2 within MLO and also for the combined three
layer MLO. 2002 illustrates the power spectral density of the SH0 layer;
2004 illustrates the power spectral density of the SH1 layer; 2006
illustrates the power spectral density of the SH2 layer, and 2008
illustrates the combined power spectral density of each layer.
[0161] Referring now to FIG. 21, there is illustrated the power spectral
density of each layer as well as the power spectral density of the
combined three layer in a log scale. 2102 represents the SH0 layer. 2104
represents the SH1 layer. 2106 represents the SH2 layer. 2108 represents
the combined layers.
[0162] Referring now to FIG. 22, there is a bandwidth efficiency
comparison versus out of band attenuation (XdB) where quantum level
overlay pulse truncation interval is [6,6] and the symbol rate is 1/6.
Referring also to FIG. 23, there is illustrated the bandwidth efficiency
comparison versus out of band attenuation (XdB) where quantum level
overlay pulse truncation interval is [6,6] and the symbol rate is 1/4.
[0163] The QLO signals are generated from the Physicist's special Hermite
functions:
f n ( t , .alpha. ) = .alpha. .pi. n ! 2 n
H n ( .alpha. t ) e  .alpha. 2 t 2 2
, .alpha. > 0 ##EQU00012##
[0164] Note that the initial hardware implementation is using
.alpha. = 1 2 ##EQU00013##
and for consistency with his part,
.alpha. = 1 2 ##EQU00014##
is used in all figures related to the spectral efficiency.
[0165] Let the lowpassequivalent power spectral density (PSD) of the
combined QLO signals be X(f) and its bandwidth be B. Here the bandwidth
is defined by one of the following criteria.
ACLR1 (First Adjacent Channel Leakage Ratio) in dBc equals:
A C L R 1 = .intg. B / 2 3 B / 2
X ( f ) df .intg.  .infin. .infin. X ( f )
df ##EQU00015##
ACLR2 (Second Adjacent Channel Leakage Ratio) in dBc equals:
A C L R 2 = .intg. 3 B / 2 5
B / 2 X ( f ) df .intg.  .infin. .infin. X (
f ) df ##EQU00016##
OutofBand Power to Total Power Ratio is:
[0166] 2 .intg. B / 2 .infin. X ( f ) df .intg.
 .infin. .infin. X ( f ) df ##EQU00017##
The BandEdge PSD in dBc/100 kHz equals:
.intg. B / 2 B 2 + 10 5 X ( f ) df .intg.
 .infin. .infin. X ( f ) df ##EQU00018##
[0167] Referring now to FIG. 24 there is illustrated a performance
comparison using ACLR1 and ACLR2 for both a square root raised cosine
scheme and a multiple layer overlay scheme. Line 2402 illustrates the
performance of a square root raised cosine 2402 using ACLR1 versus an MLO
2404 using ACLR1. Additionally, a comparison between a square root raised
cosine 2406 using ACLR2 versus MLO 2408 using ACLR2 is illustrated. Table
A illustrates the performance comparison using ACLR.
TABLEUS00001
TABLE A
Criteria:
ACLR1 .ltoreq. 30 dBc per bandwidth Spectral Efficiency
ACLR2 .ltoreq. 43 dBc per bandwidth (Symbol/sec/Hz) Gain
SRRC [8T, 8T] .beta. = 0.22 0.8765 1.0
N Symbol Duration
Layers (Tmol)
QLO N = 3 Tmol = 4 1.133 1.2926
[8, 8] N = 4 Tmol = 5 1.094 1.2481
Tmol = 4 1.367 1.5596
N = 10 Tmol = 8 1.185 1.3520
Tmol = 7 1.355 1.5459
Tmol = 6 1.580 1.8026
Tmol = 5 1.896 2.1631
Tmol = 4 2.371 2.7051
[0168] Referring now to FIG. 25, there is illustrated a performance
comparison between a square root raised cosine 2502 and a MLO 2504 using
outofband power. Referring now also to Table B, there is illustrated a
more detailed comparison of the performance using outofband power.
TABLEUS00002
TABLE B
Table 3: Performance Comparison Using OutofBand Power
Criterion:
Outofband Power/ Spectral Efficiency
Total Power .ltoreq. 30 dB (Symbol/sec/Hz) Gain
SRRC [8T, 8T] .beta. = 0.22 0.861 1.0
N Symbol Duration
Layers (Tmol)
QLO N = 3 Tmol = 4 1.080 1.2544
[8, 8] N = 4 Tmol = 5 1.049 1.2184
Tmol = 4 1.311 1.5226
N = 10 Tmol = 8 1.152 1.3380
Tmol = 7 1.317 1.5296
Tmol = 6 1.536 1.7840
Tmol = 5 1.844 2.1417
Tmol = 4 2.305 2.6771
[0169] Referring now to FIG. 26, there is further provided a performance
comparison between a square root raised cosine 2602 and a MLO 2604 using
bandedge PSD. A more detailed illustration of the performance comparison
is provided in Table C.
TABLEUS00003
TABLE C
Table 4: Performance Comparison Using BandEdge PSD
Criterion: Spectral Efficiency
BandEdge PSD = 50 dBc/100 kHz (Symbol/sec/Hz) Gain
SRRC [8T, 8T] .beta. = 0.22 0.810 1.0
N Symbol Duration
Layers (Tmol)
QLO N = 3 Tmol = 4 0.925 1.1420
[8, 8] N = 4 Tmol = 5 0.912 1.1259
Tmol = 4 1.14 1.4074
N = 10 Tmol = 8 1.049 1.2951
Tmol = 7 1.198 1.4790
Tmol = 6 1.398 1.7259
Tmol = 5 1.678 2.0716
Tmol = 4 2.097 2.5889
[0170] Referring now to FIGS. 27 and 28, there are more particularly
illustrated the transmit subsystem (FIG. 27) and the receiver subsystem
(FIG. 28). The transceiver is realized using basic building blocks
available as Commercially Off The Shelf products. Modulation,
demodulation and Special Hermite correlation and decorrelation are
implemented on a FPGA board. The FPGA board 2802 at the receiver 2800
estimated the frequency error and recovers the data clock (as well as
data), which is used to read data from the analogtodigital (ADC) board
2806. The FGBA board 2800 also segments the digital I and Q channels.
[0171] On the transmitter side 2700, the FPGA board 2702 realizes the
special hermite correlated QAM signal as well as the necessary control
signals to control the digitaltoanalog (DAC) boards 2704 to produce
analog I&Q baseband channels for the subsequent up conversion within the
direct conversion quad modulator 2706. The direct conversion quad
modulator 2706 receives an oscillator signal from oscillator 2708.
[0172] The ADC 2806 receives the I&Q signals from the quad demodulator
2808 that receives an oscillator signal from 2810.
[0173] Neither power amplifier in the transmitter nor an LNA in the
receiver is used since the communication will take place over a short
distance. The frequency band of 2.42.5 GHz (ISM band) is selected, but
any frequency band of interest may be utilized.
[0174] MIMO uses diversity to achieve some incremental spectral
efficiency. Each of the signals from the antennas acts as an independent
orthogonal channel. With QLO, the gain in spectral efficiency comes from
within the symbol and each QLO signal acts as independent channels as
they are all orthogonal to one another in any permutation. However, since
QLO is implemented at the bottom of the protocol stack (physical layer),
any technologies at higher levels of the protocol (i.e. Transport) will
work with QLO. Therefore one can use all the conventional techniques with
QLO. This includes RAKE receivers and equalizers to combat fading,
cyclical prefix insertion to combat time dispersion and all other
techniques using beam forming and MIMO to increase spectral efficiency
even further.
[0175] When considering spectral efficiency of a practical wireless
communication system, due to possibly different practical bandwidth
definitions (and also not strictly bandlimited nature of actual transmit
signal), the following approach would be more appropriate.
[0176] Referring now to FIG. 29, consider the equivalent discrete time
system, and obtain the Shannon capacity for that system (will be denoted
by Cd). Regarding the discrete time system, for example, for conventional
QAM systems in AWGN, the system will be:
y[n]=ax[n]+w[n]
where a is a scalar representing channel gain and amplitude scaling, x[n]
is the input signal (QAM symbol) with unit average energy (scaling is
embedded in a), y[n] is the demodulator (matched filter) output symbol,
and index n is the discrete time index.
[0177] The corresponding Shannon capacity is:
C.sub.d=log.sub.2(1+a.sup.2/.sigma..sup.2)
where .sigma.2 is the noise variance (in complex dimension) and
a.sup.2/.sigma..sup.2 is the SNR of the discrete time system.
[0178] Second, compute the bandwidth W based on the adopted bandwidth
definition (e.g., bandwidth defined by 40 dBc out of band power). If the
symbol duration corresponding to a sample in discrete time (or the time
required to transmit C.sub.d bits) is T, then the spectral efficiency can
be obtained as:
C/W=C.sub.d/(TW)bps/Hz
[0179] In discrete time system in AWGN channels, using Turbo or similar
codes will give performance quite close to Shannon limit C.sub.d. This
performance in discrete time domain will be the same regardless of the
pulse shape used. For example, using either SRRC (square root raised
cosine) pulse or a rectangle pulse gives the same C.sub.d (or C.sub.d/T).
However, when we consider continuous time practical systems, the
bandwidths of SRRC and the rectangle pulse will be different. For a
typical practical bandwidth definition, the bandwidth for a SRRC pulse
will be smaller than that for the rectangle pulse and hence SRRC will
give better spectral efficiency. In other words, in discrete time system
in AWGN channels, there is little room for improvement. However, in
continuous time practical systems, there can be significant room for
improvement in spectral efficiency.
[0180] Referring now to FIG. 30, there is illustrated a PSD plot (BLANK)
of MLO, modified MLO (MMLO) and square root raised cosine (SRRC). From
the illustration in FIG. 30, demonstrates the better localization
property of MLO. An advantage of MLO is the bandwidth. FIG. 30 also
illustrates the interferences to adjacent channels will be much smaller
for MLO. This will provide additional advantages in managing, allocating
or packaging spectral resources of several channels and systems, and
further improvement in overall spectral efficiency. If the bandwidth is
defined by the 40 dBc out of band power, the withinbandwidth PSDs of
MLO and SRRC are illustrated in FIG. 31. The ratio of the bandwidths is
about 1.536. Thus, there is significant room for improvement in spectral
efficiency.
[0181] Modified MLO systems are based on blockprocessing wherein each
block contains N MLO symbols and each MLO symbol has L layers. MMLO can
be converted into parallel (virtual) orthogonal channels with different
channel SNRs as illustrated in FIG. 32. The outputs provide equivalent
discrete time parallel orthogonal channels of MMLO.
[0182] Note that the intersymbol interference caused pulse overlapping of
MLO has been addressed by the parallel orthogonal channel conversion. As
an example, the power gain of a parallel orthogonal virtual channel of
MMLO with three layers and 40 symbols per block is illustrated in FIG.
33. FIG. 33 illustrates the channel power gain of the parallel orthogonal
channels of MMLO with three layers and T.sub.sim=3. By applying a water
filling solution, an optimal power distribution across the orthogonal
channels for a fixed transmit power may be obtained. The transmit power
on the k.sup.th orthogonal channel is denoted by P.sub.k. Then the
discrete time capacity of the MMLO can be given by:
C d + k = 1 k log 2 ( 1 + P k a k 2
.sigma. k 2 ) bits per block ##EQU00019##
[0183] Note that K depends on the number of MLO layers, the number of MLO
symbols per block, and MLO symbol duration.
[0184] For MLO pulse duration defined by [t.sub.i, t.sub.i], and symbol
duration T.sub.mlo, the MMLO block length is:
T.sub.block=(N1)T.sub.mlo+2t.sub.1
[0185] Suppose the bandwidth of MMLO signal based on the adopted bandwidth
definition (ACLR, OBP, or other) is W.sub.mmlo, then the practical
spectral efficiency of MMLO is given by:
C d W mmlo T block = 1 W mmlo { ( N  1 ) T
mlo + 2 t 1 } k = 1 K log 2 ( 1 + P k
a k 2 .sigma. k 2 ) bp s Hz ##EQU00020##
[0186] FIGS. 3435 show the spectral efficiency comparison of MMLO with
N=40 symbols per block, L=3 layers, T.sub.mlo=3, t.sub.1=8, and SRRC with
duration [8T, 8T], T=1, and the rolloff factor .beta.=0.22, at SNR of 5
dB. Two bandwidth definitions based on ACLR1 (first adjacent channel
leakage power ratio) and OBP (out of band power) are used.
[0187] FIGS. 3637 show the spectral efficiency comparison of MMLO with
L=4 layers. The spectral efficiencies and the gains of MMLO for specific
bandwidth definitions are shown in the following tables.
TABLEUS00004
TABLE D
Spectral Efficiency (bps/Hz) Gain with
based on ACLR1 .ltoreq. 30 dBc reference
per bandwidth to SRRC
SRRC 1.7859 1
MMLO (3 layers, Tmlo = 3) 2.7928 1.5638
MMLO (4 layers, Tmlo = 3) 3.0849 1.7274
TABLEUS00005
TABLE E
Gain with
Spectral Efficiency (bps/Hz) reference
based on OBP .ltoreq. 40 dBc to SRRC
SRRC 1.7046 1
MMLO (3 layers, Tmlo = 3) 2.3030 1.3510
MMLO (4 layers, Tmlo = 3) 2.6697 1.5662
[0188] Referring now to FIGS. 38 and 39, there are provided basic block
diagrams of lowpassequivalent MMLO transmitters (FIG. 38) and receivers
(FIG. 39). The lowpassequivalent MMLO transmitter 3800 receives a
number of input signals 3802 at a blockbased transmitter processing
3804. The transmitter processing outputs signals to the SH(L1) blocks
3806 which produce the I&Q outputs. These signals are then all combined
together at a combining circuit 3808 for transmission.
[0189] Within the baseband receiver (FIG. 39) 3900, the received signal is
separated and applied to a series of match filters 3902. The outputs of
the match filters are then provided to the blockbased receiver
processing block 3904 to generate the various output streams.
[0190] Consider a block of N MLOsymbols with each MLO symbol carrying L
symbols from L layers. Then there are NL symbols in a block. Define c(m,
n)=symbol transmitted by the mth MLO layer at the nth MLO symbol. Write
all NL symbols of a block as a column vector as follows: c=[c(0,0),
c(1,0), . . . , c(L1, 0), c(0,1), c(1,1), . . . , c(L1, 1), . . . ,
c(L1, N1)]T. Then the outputs of the receiver matched filters for that
transmitted block in an AWGN channel, defined by the column vector y of
length NL, can be given as y=H c+n, where H is an NL.times.NL matrix
representing the equivalent MLO channel, and n is a correlated Gaussian
noise vector.
[0191] By applying SVD to H, we have H=U D VH where D is a diagonal matrix
containing singular values. Transmitter side processing using V and the
receiver side processing UH, provides an equivalent system with NL
parallel orthogonal channels, (i.e., y=H Vc+n and UH y=Dc+UH n). These
parallel channel gains are given by diagonal elements of D. The channel
SNR of these parallel channels can be computed. Note that by the transmit
and receive blockbased processing, we obtain parallel orthogonal
channels and hence the ISI issue has be resolved.
[0192] Since the channel SNRs of these parallel channels are not the same,
we can apply the optimal Water filling solution to compute the transmit
power on each channel given a fixed total transmit power. Using this
transmit power and corresponding channel SNR, we can compute capacity of
the equivalent system as given in the previous report.
Issues of Fading, Multipath, and MultiCell Interference
[0193] Techniques used to counteract channel fading (e.g., diversity
techniques) in conventional systems can also be applied in MMLO. For
slowlyvarying multipath dispersive channels, if the channel impulse
response can be fed back, it can be incorporated into the equivalent
system mentioned above, by which the channel induced ISI and the
intentionally introduced MMLO ISI can be addressed jointly. For fast
timevarying channels or when channel feedback is impossible, channel
equalization needs to be performed at the receiver. A blockbased
frequencydomain equalization can be applied and an oversampling would be
required.
[0194] If we consider the same adjacent channel power leakage for MMLO and
the conventional system, then the adjacent cells' interference power
would be approximately the same for both systems. If interference
cancellation techniques are necessary, they can also be developed for
MMLO.
Scope and System Description
[0195] This report presents the symbol error probability (or symbol error
rate) performance of MLO signals in additive white Gaussian noise channel
with various intersymbol interference levels. As a reference, the
performance of the conventional QAM without ISI is also included. The
same QAM size is considered for all layers of MLO and the conventional
QAM.
[0196] The MLO signals are generated from the Physicist's special Hermite
functions:
f n ( t , .alpha. ) = .alpha. .pi. n ! 2 n
H n ( .alpha. t ) e  .alpha. 2 t 2 2
##EQU00021##
where Hn(.alpha.t) is the n.sup.th order Hermite polynomial. Note that
the functions used in the lab setup correspond to
.alpha. = 1 2 ##EQU00022##
and, for consistency,
.alpha. = 1 2 ##EQU00023##
is used in this report.
[0197] MLO signals with 3, 4 or 10 layers corresponding to n=0.about.2,
0.about.3, or 0.about.9 are used and the pulse duration (the range of t)
is [8, 8] in the above function.
[0198] AWGN channel with perfect synchronization is considered.
[0199] The receiver consists of matched filters and conventional detectors
without any interference cancellation, i.e., QAM slicing at the matched
filter outputs.
% pulse  overlapping = T p  T sym T p
.times. 100 % ##EQU00024##
where Tp is the pulse duration (16 in the considered setup) and Tsym is
the reciprocal of the symbol rate in each MLO layer. The considered cases
are listed in the following table.
TABLEUS00006
TABLE F
% of Pulse Overlapping T.sub.sym T.sub.p
0% 16 16
12.5% 14 16
18.75% 13 16
.sup. 25% 12 16
37.5% 10 16
43.75% 9 16
.sup. 50% 8 16
56.25% 7 16
62.5% 6 16
.sup. 75% 4 16
Derivation of the Signals Used in Modulation
[0200] To do that, it would be convenient to express signal amplitude s(t)
in a complex form close to quantum mechanical formalism. Therefore the
complex signal can be represented as:
.psi. ( t ) = s ( t ) + j .sigma. ( t )
##EQU00025## where s ( t ) .ident. real signal
##EQU00025.2## .sigma. ( t ) = imaginary signal (
quadrature ) ##EQU00025.3## .sigma. ( t ) = 1 .pi.
.intg.  .infin. .infin. s ( .tau. ) d .tau.
.tau.  t s ( t ) =  1 .pi. .intg.  .infin.
.infin. .sigma. ( t ) d.tau. .tau.  t
##EQU00025.4##
Where s(t) and .sigma.(t) are Hilbert transforms of one another and since
.sigma.(t) is qudratures of s(t), they have similar spectral components.
That is if they were the amplitudes of sound waves, the ear could not
distinguish one form from the other.
[0201] Let us also define the Fourier transform pairs as follows:
.psi. ( t ) = 1 .pi. .intg.  .infin. .infin. .PHI.
( f ) e j .omega.t df ##EQU00026## .PHI. (
f ) = 1 .pi. .intg.  .infin. .infin. .psi. ( t )
e  j .omega.t dt ##EQU00026.2## .psi. * ( t )
.psi. ( t ) = [ s ( t ) ] 2 + [ .sigma. ( t
) ] 2 + .ident. signal power ##EQU00026.3##
[0202] Let's also normalize all moments to M.sub.0:
M 0 = .intg. 0 .tau. s ( t ) dt ##EQU00027## M 0
= .intg. 0 .tau. .PHI. .PHI. df ##EQU00027.2##
[0203] Then the moments are as follows:
M 0 = .intg. 0 .tau. s ( t ) dt ##EQU00028## M 1
= .intg. 0 .tau. ts ( t ) dt ##EQU00028.2## M 2 =
.intg. 0 .tau. t 2 s ( t ) dt ##EQU00028.3## M N 
1 = .intg. 0 .tau. t N  1 s ( t ) dt
##EQU00028.4##
[0204] In general, one can consider the signal s(t) be represented by a
polynomial of order N, to fit closely to s(t) and use the coefficient of
the polynomial as representation of data. This is equivalent to
specifying the polynomial in such a way that its first N "moments"
M.sub.J shall represent the data. That is, instead of the coefficient of
the polynomial, we can use the moments. Another method is to expand the
signal s(t) in terms of a set of N orthogonal functions .phi..sub.k(t),
instead of powers of time. Here, we can consider the data to be the
coefficients of the orthogonal expansion. One class of such orthogonal
functions are sine and cosine functions (like in Fourier series).
[0205] Therefore we can now represent the above moments using the
orthogonal function .psi. with the following moments:
t _ = .intg. .psi. ( t ) t .psi. ( t )
dt .intg. .psi. ( t ) .psi. ( t ) dt
##EQU00029## t 2 _ = .intg. .psi. ( t ) t 2
.psi. ( t ) dt .intg. .psi. ( t ) .psi. ( t
) dt ##EQU00029.2## t n _ = .intg. .psi. ( t )
t n .psi. ( t ) dt .intg. .psi. ( t )
.psi. ( t ) dt ##EQU00029.3##
Similarly,
[0206] f _ = .intg. .PHI. ( f ) f .PHI.
( f ) df .intg. .PHI. ( f ) .PHI. ( f ) df
##EQU00030## f 2 _ = .intg. .PHI. ( f ) f 2
.PHI. ( f ) df .intg. .PHI. ( f ) .PHI. ( f
) df ##EQU00030.2## f n _ = .intg. .PHI. ( f )
f n .PHI. ( f ) df .intg. .PHI. ( f )
.PHI. ( f ) df ##EQU00030.3##
If we did not use complex signal, then:
f=0
To represent the mean values from time to frequency domains, replace:
.PHI. ( f ) .fwdarw. .psi. ( t ) ##EQU00031## f .fwdarw.
1 2 .pi. j d dt ##EQU00031.2##
These are equivalent to somewhat mysterious rule in quantum mechanics
where classical momentum becomes an operator:
P x .fwdarw. h 2 .pi. j .differential.
.differential. x ##EQU00032##
Therefore using the above substitutions, we have:
f _ = .intg. .PHI. ( f ) f .PHI. ( f )
df .intg. .PHI. ( f ) .PHI. ( f ) df =
.intg. .psi. ( t ) ( 1 2 .pi. j )
d .psi. ( t ) dt dt .intg. .psi. ( t )
.psi. ( t ) dt = ( 1 2 .pi. j )
.intg. .psi. d .psi. dt dt .intg. .psi.
.psi. dt And : f 2 _ =
.intg. .PHI. ( f ) f 2 .PHI. ( f ) df
.intg. .PHI. ( f ) .PHI. ( f ) df =
.intg. .psi. ( 1 2 .pi. j ) 2 d 2
dt 2 .psi.dt .intg. .psi. .psi. dt = 
( 1 2 .pi. ) 2 .intg. .psi. d 2 dt 2
.psi. dt .intg. .psi. .psi. dt t
2 = .intg. .psi. t 2 .psi. dt .intg.
.psi. .psi. dt ##EQU00033##
We can now define an effective duration and effective bandwidth as:
.DELTA. t = 2 .pi. ( t  t _ ) 2 _ = 2
.pi. rms in time ##EQU00034## .DELTA. f =
2 .pi. ( f  f _ ) 2 _ = 2 .pi. rms in
frequency ##EQU00034.2##
But we know that:
( t  t _ ) 2 _ = t 2 _  ( t _ ) 2 ##EQU00035##
( f  f _ ) 2 _ = f 2 _  ( f _ ) 2
##EQU00035.2##
We can simplify if we make the following substitutions:
.tau.=tt
.PSI.(.tau.)=.psi.(t).sub.e.sup.j.omega..tau.
.omega..sub.0=.omega.=2.pi.f=2.pi.f.sub.0
[0207] We also know that:
(.DELTA.t).sup.2(.DELTA.f).sup.2=(.DELTA.t.DELTA.f).sup.2
And therefore:
( .DELTA. t .DELTA. f ) 2 = 1 4 [ 4
.intg. .PSI. ( .tau. ) .tau. 2 .PSI. ( .tau. ) d
.tau. .intg. d .PSI. d .tau.
d .PSI. d .tau. d .tau. ( .intg.
.PSI. ( .tau. ) .psi. ( .tau. ) d .tau. ) 2
] .gtoreq. ( 1 4 ) ##EQU00036## ( .DELTA. t
.DELTA. f ) .gtoreq. ( 1 2 ) ##EQU00036.2##
Now instead of (.DELTA.t .DELTA.f).gtoreq.(1/2) we are interested to
force the equality (.DELTA.t .DELTA.f)=(1/2) and see what signals satisfy
the equality. Given the fixed bandwidth .DELTA.f, the most efficient
transmission is one that minimizes the timebandwidth product (.DELTA.t
.DELTA.f)=(1/2) For a given bandwidth .DELTA.f, the signal that minimizes
the transmission in minimum time will be a Gaussian envelope. However, we
are often given not the effective bandwidth, but always the total
bandwidth f.sub.2f.sub.1. Now, what is the signal shape which can be
transmitted through this channel in the shortest effective time and what
is the effective duration?
.DELTA. t 1 ( 2 .pi. ) 2 .intg. f 1 f 2
d .PHI. df d .PHI. df .intg. f
1 f 2 .PHI. .PHI. df .fwdarw. min ##EQU00037##
Where .phi.(f) is zero outside the range f.sub.2f.sub.1.
[0208] To do the minimization, we would use the calculus of variations
(Lagrange's Multiplier technique). Note that the denominator is constant
and therefore we only need to minimize the numerator as:
.DELTA. t .fwdarw. min .fwdarw. .delta. .intg. f 1 f
2 ( d .PHI. df d .PHI. df +
.LAMBDA..PHI. .PHI. ) df = 0 ##EQU00038## First
Trem ##EQU00038.2## .delta. .intg. f 1 f 2 d
.PHI. df d .PHI. df df = .intg. (
d .PHI. df .delta. d .PHI. df + d
.PHI. df .delta. d .PHI. df ) df =
.intg. ( d .PHI. df d .delta.
.PHI. df + d .PHI. df d .delta.
.PHI. df ) df = [ d .PHI. df
.delta..PHI. d .PHI. df .delta..PHI. ] f 1 f 2
 .intg. ( d 2 .PHI. df 2
.delta..PHI. + d 2 .PHI. df 2
.delta..PHI. ) df = .intg. ( d 2 .PHI.
df 2 .delta..PHI. + d 2 .PHI.
df 2 .delta..PHI. ) df ##EQU00038.3##
Second Trem ##EQU00038.4## .delta. .intg. f 1 f 2
( .LAMBDA..PHI. .PHI. ) df = .LAMBDA. .intg. f 1 f
2 ( .PHI. .delta..PHI. + .PHI..delta..PHI. ) df
##EQU00038.5## Both Trems = .intg. [ ( d
2 .PHI. df 2 + .LAMBDA..PHI. ) .delta..PHI.
+ ( d 2 .PHI. df 2 + .LAMBDA..PHI. )
.delta..PHI. ] df = 0 ##EQU00038.6##
This is only possible if and only if:
( d 2 .PHI. df 2 + .LAMBDA..PHI. ) = 0
##EQU00039##
The solution to this is of the form
.PHI. ( f ) = sin k .pi. ( f  f 1 f 2
 f 1 ) ##EQU00040##
Now if we require that the wave vanishes at infinity, but still satisfy
the minimum timebandwidth product:
(.DELTA.t.DELTA.f)=(1/2)
Then we have the wave equation of a Harmonic Oscillator:
d 2 .PSI. ( .tau. ) d .tau. 2 + (
.lamda.  .alpha. 2 .tau. 2 ) .PSI. ( .tau. ) = 0
##EQU00041##
which vanishes at infinity only if:
.lamda. = .alpha. ( 2 n + 1 ) ##EQU00042## .psi. n =
e  1 2 .omega. 2 .tau. 2 d n d .tau. n
e  .alpha. 2 .tau. 2 .varies. H n ( .tau. )
##EQU00042.2##
Where H.sub.n(.tau.) is the Hermit functions and:
(.DELTA.t .DELTA.f)=1/2(2n+1)
So Hermit functions H.sub.n(.tau.) occupy information blocks of 1/2, 3/2,
5/2, . . . with 1/2 as the minimum information quanta.
Squeezed States
[0209] Here we would derive the complete Eigen functions in the most
generalized form using quantum mechanical approach of Dirac algebra. We
start by defining the following operators:
b = m .omega. ' 2 ( x + ip m
.omega. ' ) ##EQU00043## b + = m .omega. ' 2
( x  ip m .omega. ' ) [ b , b + ] =
1 ##EQU00043.2## a = .lamda. b  .mu. b +
##EQU00043.3## a + = .lamda. b +  .mu. b
##EQU00043.4##
Now we are ready to define .DELTA.x and .DELTA.p as:
( .DELTA. x ) 2 = 2 m .omega. (
.omega. .omega. ' ) = 2 m .omega. ( .lamda. 
.mu. ) 2 ##EQU00044## ( .DELTA. p ) 2 =
m .omega. 2 ( .omega. ' .omega. ) = m
.omega. 2 ( .lamda. + .mu. ) 2 ##EQU00044.2## (
.DELTA. x ) 2 ( .DELTA. p ) 2 = 2 4
( .lamda. 2  .mu. 2 ) 2 ##EQU00044.3## .DELTA. x
.DELTA. p = 2 ( .lamda. 2  .mu. 2 ) = 2
##EQU00044.4##
Now let parameterize differently and instead of two variables .lamda. and
.mu., we would use only one variable .xi. as follows:
.lamda.=sin h.xi.
.mu.=cos h.xi.
.lamda.+.mu.=e.sup..xi.
.lamda..mu.=e.sup..xi.
b .beta. = .beta. .beta. ##EQU00045## (
.lamda. a + .mu. a + ) .beta. = .beta.
.beta. ##EQU00045.2## b = U a U +
##EQU00045.3## U = e .xi. / 2 ( a 2  a + 2 )
##EQU00045.4## U + ( .xi. ) aU ( .xi. ) = a
cosh .xi.  a + sinh .xi. ##EQU00045.5## U +
( .xi. ) a + U ( .xi. ) = a + cosh
.xi.  a sinh .xi. ##EQU00045.6##
We can now consider the squeezed operator:
.alpha. , .xi. = U ( .xi. ) D ( .alpha. ) 0
##EQU00046## D ( .alpha. ) = e  .alpha. 2 2 e
.alpha. a + e  .alpha. * a ##EQU00046.2##
.alpha. = n = 0 .infin. .alpha. n n ! e 
.alpha. 2 2 n ##EQU00046.3## .alpha. = e 
.alpha. 2 2 + .alpha. a + 0 ##EQU00046.4##
For a distribution P(n) we would have:
P ( n ) = n .beta. , .xi. 2 ##EQU00047##
.alpha. .beta. , .xi. = n = 0 .infin.
.alpha. n n ! e  .alpha. 2 2 n .beta.
, .xi. ##EQU00047.2## e 2 zt  t 2 = n = 0
.infin. H n ( z ) t n n ! ##EQU00047.3##
Therefore the final result is:
n .beta. , .xi. = ( tanh .xi. ) n /
2 2 n / 2 ( n ! cosh .xi. ) 2 e  1 /
2 ( .beta. 2  .beta. 2 tanh .xi. ) H n
( .beta. 2 sinh .xi. cosh .xi. )
##EQU00048##
[0210] Optical Fiber Communications
[0211] The use of orbital angular momentum and multiple layer overlay
modulation processing techniques within an optical communications
interface environment as described with respect to FIG. 3 can provide a
number of opportunities within the optical communications environment for
enabling the use of the greater signal bandwidths provided by the use of
optical orbital angular momentum processing, or multiple layer overlay
modulation techniques alone. FIG. 40 illustrates the general
configuration of an optical fiber communication system. The optical fiber
communication system 4000 includes an optical transmitter 4002 and an
optical receiver 4004. The transmitter 4002 and receiver 4004 communicate
over an optical fiber 4006. The transmitter 4002 includes information
within a light wavelength or wavelengths that is propagated over the
optical fiber 4006 to the optical receiver 4004.
[0212] Optical communications network traffic has been steadily increasing
by a factor of 100 every decade. The capacity of single mode optical
fibers has increased 10,000 times within the last three decades.
Historically, the growth in the bandwidth of optical fiber communications
has been sustained by information multiplexing techniques using
wavelength, amplitude, phase, and polarization of light as a means for
encoding information. Several major discoveries within the fiberoptics
domain have enabled today's optical networks. An additional discovery was
led by Charles M. Kao's groundbreaking work that recognized glass
impurities within an optical fiber as a major signal loss mechanism.
Existing glass losses at the time of his discovery were approximately 200
dB per kilometer at 1 micrometer.
[0213] These discoveries gave birth to optical fibers and led to the first
commercial optical fibers in the 1970s, having an attenuation low enough
for communication purposes in the range of approximately 20 dBs per
kilometer. Referring now to FIGS. 41A41C, there is more particularly
illustrated the single mode fiber 4102, multicore fibers 4108, and
multimode fibers 4110 described herein above. The multicore fibers 4108
consist of multiple cores 4112 included within the cladding 4113 of the
fiber. As can be seen in FIG. 41B, there are illustrated a 3 core fiber,
7 core fiber, and 19 core fiber. Multimode fibers 4110 comprise multimode
fibers comprising a few mode fiber 4120 and a multimode fiber 4122.
Finally, there is illustrated a hollow core fiber 4115 including a hollow
core 4114 within the center of the cladding 4116 and sheathing 4118. The
development of single mode fibers (SMF) such as that illustrated at 4102
(FIG. 41A) in the early 1980s reduced pulse dispersion and led to the
first fiberoptic based transAtlantic telephone cable. This single mode
fiber included a single transmission core 4104 within an outer sheathing
4106. Development of indium gallium arsenide photodiodes in the early
1990s shifted the focus to nearinfrared wavelengths (1550 NM), were
silica had the lowest loss, enabling extended reach of the optical
fibers. At roughly the same time, the invention of erbiumdoped fiber
amplifiers resulted in one of the biggest leaps in fiber capacity within
the history of communication, a thousand fold increase in capacity
occurred over a 10 year period. The development was mainly due to the
removed need for expensive repeaters for signal regeneration, as well as
efficient amplification of many wavelengths at the same time, enabling
wave division multiplexing (WDM).
[0214] Throughout the 2000s, increases in bandwidth capacity came mainly
from introduction of complex signal modulation formats and coherent
detection, allowing information encoding using the phase of light. More
recently, polarization division multiplexing (PDM) doubled channel
capacity. Through fiber communication based on SMFs featured tremendous
growth in the last three decades, recent research has indicated SMF
limitations. Nonlinear effects in silica play a significant role in long
range transmission, mainly through the Kerr effect, where a presence of a
channel at one wavelength can change the refractive index of a fiber,
causing distortions of other wavelength channels. More recently, a
spectral efficiency (SE) or bandwidth efficiency, referring to the
transmitted information rate over a given bandwidth, has become
theoretically analyzed assuming nonlinear effects in a noisy fiber
channel. This research indicates a specific spectral efficiency limit
that a fiber of a certain length can reach for any signal to noise (SNR).
Recently achieved spectral efficiency results indeed show that the
proximity to the spectral efficiency limit, indicating the need for new
technologies to address the capacity issue in the future.
[0215] Among several possible directions for optical communications in the
future, the introduction of new optical fibers 4006 other than single
mode fibers 4102 has shown promising results. In particular, researchers
have focused on spatial dimensions in new fibers, leading to socalled
space division multiplexing (SDM) where information is transmitted using
cores of multicore fibers (MCF) 4108 (FIG. 41B) or mode division
multiplexing (MDM) or information is transmitted using modes of multimode
fibers (MMFs) 4110 (FIG. 41C). The latest results show spectral
efficiency of 91 bits/S/Hz using 12 core multicore fiber 4108 for 52
kilometer long fibers and 12 bits/S/Hz using 6 mode multimode fiber 4110
and 112 kilometer long fibers. Somewhat unconventional transmissions at
2.08 micrometers have also been demonstrated in two 90 meter long
photonic crystal fibers, though these fibers had high losses of 4.5
decibels per kilometer.
[0216] While offering promising results, these new types of fibers have
their own limitations. Being noncircularly symmetric structures,
multicore fibers are known to require more complex, expensive
manufacturing. On the other hand, multimode fibers 4110 are easily
created using existing technologies. However, conventional multimode
fibers 4110 are known to suffer from mode coupling caused by both random
perturbations in the fibers and in modal multiplexers/demultiplexers.
[0217] Several techniques have been used for mitigating mode coupling. In
a strong coupling regime, modal cross talk can be compensated using
computationally intensive multiinput multioutput (MIMO) digital signal
processing (DSP). While MIMO DSP leverages the technique's current
success in wireless networks, the wireless network data rates are several
orders of magnitude lower than the ones required for optical networks.
Furthermore, MIMO DSP complexity inevitably increases with an increasing
number of modes and no MIMO based data transmission demonstrations have
been demonstrated in real time thus far. Furthermore, unlike wireless
communication systems, optical systems are further complicated because of
fiber's nonlinear effects. In a weak coupling regime, where cross talk is
smaller, methods that also use computationally intensive adapted optics,
feedback algorithms have been demonstrated. These methods reverse the
effects of mode coupling by sending a desired superposition of modes at
the input, so that desired output modes can be obtained. This approach is
limited, however, since mode coupling is a random process that can change
on the order of a millisecond in conventional fibers.
[0218] Thus, the adaptation of multimode fibers 4110 can be problematic in
long haul systems where the round trip signal propagation delay can be
tens of milliseconds. Though 2.times.56 GB/S transmission at 8 kilometers
length has been demonstrated in the case of two higher order modes, none
of the adaptive optics MDM methods to date have demonstrated for more
than two modes. Optical fibers act as wave guides for the information
carrying light signals that are transmitted over the fiber. Within an
ideal case, optical fibers are 2D, cylindrical wave guides comprising one
or several cores surrounded by a cladding having a slightly lower
refractive index as illustrated in FIGS. 41A41D. A fiber mode is a
solution (an eigenstate) of a wave guide equation describing the field
distribution that propagates within a fiber without changing except for
the scaling factor. All fibers have a limit on the number of modes that
they can propagate, and have both spatial and polarization degrees of
freedom.
[0219] Single mode fibers (SMFs) 4102 is illustrated in FIG. 41A support
propagation of two orthogonal polarizations of the fundamental mode only
(N=2). For sufficiently large core radius and/or the core cladding
difference, a fiber is multimoded for N>2 as illustrated in FIG. 41C.
For optical signals having orbital angular momentums and multilayer
modulation schemes applied thereto, multimode fibers 4110 that are weakly
guided may be used. Weakly guided fibers have a core cladding refractive
index difference that is very small. Most glass fibers manufactured today
are weakly guided, with the exception of some photonic crystal fibers and
aircore fibers. Fiber guide modes of multimode fibers 4110 may be
associated in step indexed groups where, within each group, modes
typically having similar effective indexes are grouped together. Within a
group, the modes are degenerate. However, these degeneracies can be
broken in a certain fiber profile design.
[0220] We start by describing translationally invariant waveguide with
refractive index n=n(x, y), with n.sub.co being maximum refractive index
("core" of a waveguide), and n.sub.cl being refractive index of the
uniform cladding, and .rho. represents the maximum radius of the
refractive index n. Due to translational invariance the solutions (or
modes) for this waveguide can be written as:
E.sub.j(x,y,z)=e.sub.j(x,y)e.sup.i.beta..sup.j.sup.z,
H.sub.j(x,y,z)=h.sub.j(x,y)e.sup.i.beta..sup.j.sup.z,
where .beta..sub.j is the propagation constant of the jth mode. Vector
wave equation for source free Maxwell's equation can be written in this
case as:
(.gradient..sup.2+n.sup.2k.sup.2.beta.f)e.sub.j=(.gradient..sub.ti.bet
a..sub.j{tilde over (z)})(e.sub.tf.gradient..sup.t ln(n.sup.2))
(.gradient..sup.2+n.sup.2k.sup.2.beta..sub.j.sup.2)h.sub.j=.gradient..s
ub.t ln(n.sup.2))x([[.gradient.]]c+t.beta..sub.j{circumflex over
(z)})xk.sub.l)
where k=2.pi./.lamda. is the freespace wavenumber, .lamda. is a
freespace wavelength, e.sub.t=e.sub.x{circumflex over (x)}+e.sub.yy is a
transverse part of the electric field, .gradient..sup.2 is a transverse
Laplacian and .gradient..sub.t transverse vector gradient operator.
Waveguide polarization properties are built into the wave equation
through the .gradient..sub.t ln(n.sup.2) terms and ignoring them would
lead to the scalar wave equation, with linearly polarized modes. While
previous equations satisfy arbitrary waveguide profile n(x, y), in most
cases of interest, profile height parameter .DELTA. can be considered
small .DELTA.<<1, in which case waveguide is said to be weakly
guided, or that weakly guided approximation (WGA) holds. If this is the
case, a perturbation theory can be applied to approximate the solutions
as:
E ( x , y , z ) = e ( x , y ) e i ( .beta. +
.beta. ~ ) z = ( e t + z ^ e z ) e i
( .beta. + .beta. ~ ) z ##EQU00049## H ( x , y , z
) = h ( x , y ) e i ( .beta. + .beta. ~ ) z
= ( h t + z ^ h z ) e i ( .beta. + .beta.
~ ) z ##EQU00049.2##
where subscripts t and z denote transverse and longitudinal components
respectively. Longitudinal components can be considered much smaller in
WGA and we can approximate (but not neglect) them as:
e z = t ( 2 .DELTA. ) 1 2 V ( .rho.
.DELTA. t e t ) ##EQU00050## h z = t ( 2
.DELTA. ) 1 2 V ( .rho. .DELTA. t h t )
##EQU00050.2##
Where .DELTA. and V are profile height and fiber parameters and
transversal components satisfy the simplified wave equation.
(V.sup.2+n.sup.2k.sup.2.beta..sub.j.sup.2)e.sub.j=0
Though WGA simplified the waveguide equation, further simplification can
be obtained by assuming circularly symmetric waveguide (such as ideal
fiber). If this is the case refractive index that can be written as:
n(r)=n.sup.2.sub.co(12f(R).DELTA.)
where f(R).gtoreq.0 is a small arbitrary profile variation.
[0221] For a circularly symmetric waveguide, we would have propagation
constants .beta..sub.lm that are classified using azimuthal (l) and
radial (m) numbers. Another classification uses effective indices
n.sub.lm (sometimes noted as n.sup.eff.sub.lm or simply n.sub.eff, that
are related to propagation constant as: .beta..sub.lm=kn.sup.ef f). For
the case of l=0, the solutions can be separated into two classes that
have either transverse electric (T E.sub.0m) or transverse magnetic (T
M.sub.0m) fields (called meridional modes). In the case of l.noteq.0,
both electric and magnetic field have zcomponent, and depending on which
one is more dominant, socalled hybrid modes are denoted as: HE.sub.lm
and EH.sub.lm.
[0222] Polarization correction .delta..beta. has different values within
the same group of modes with the same orbital number (l), even in the
circularly symmetric fiber. This is an important observation that led to
development of a special type of fiber.
[0223] In case of a step refractive index, solutions are the Bessel
functions of the first kind, J.sub.l(r), in the core region, and modified
Bessel functions of the second kind, K.sub.l(r), in the cladding region.
[0224] In the case of stepindex fiber the groups of modes are almost
degenerate, also meaning that the polarization correction .delta..beta.
can be considered very small. Unlike HE.sub.11 modes, higher order modes
(HOMs) can have elaborate polarizations. In the case of circularly
symmetric fiber, the odd and even modes (for example HE.sup.odd and
HE.sup.even modes) are always degenerate (i.e. have equal n.sub.eff),
regardless of the index profile. These modes will be nondegenerate only
in the case of circularly asymmetric index profiles.
[0225] Referring now to FIG. 42, there are illustrated the first six modes
within a step indexed fiber for the groups L=0 and L=1.
[0226] When orbital angular momentums are applied to the light wavelength
within an optical transmitter of an optical fiber communication system,
the various orbital angular momentums applied to the light wavelength may
transmit information and be determined within the fiber mode.
[0227] Angular momentum density (M) of light in a medium is defined as:
M = 1 c 2 r .times. ( E .times. H ) = r .times. P = 1
c 2 r .times. S ##EQU00051##
with r as position, E electric field, H magnetic field, P linear momentum
density and S Poynting vector.
[0228] The total angular momentum (J), and angular momentum flux
(.PHI..sub.M) can be defined as:
l=.intg..intg..intg.MdV
.PHI..sub.M=.intg..intg.MdA
[0229] In order to verify whether certain mode has an OAM let us look at
the time averages of the angular momentum flux .PHI..sub.M:
(.PHI..sub.M)=.intg..intg.<M>dA
as well as the time average of the energy flux:
( .PHI. W ) = .intg. .intg. S z 0 dA ##EQU00052##
[0230] Because of the symmetry of radial and axial components about the
fiber axis, we note that the integration in equation will leave only
zcomponent of the angular momentum density non zero. Hence:
( M ) = ( M ) z = 1 c 2 r .times. ( E .times. H ) z
##EQU00053##
and knowing (S)=Re{S} and S=1/2E.times.H* leads to:
S.sub..phi.=1/2(E.sub.yH.sub.z*+E.sub.zH.sub.r*)
S.sub.z=1/2(E.sub.wH.sub.y*E.sub.yH.sub.x*)
[0231] Let us now focus on a specific linear combination of the
HE.sub.l+1,m.sup.even and HE.sub.l+1,m.sup.odd modes with .pi./2 phase
shift among them:
V.sub.lm.sup.+=HE.sub.l+1,m.sup.even+lEH.sub.l+1,m.sup.odd
[0232] The idea for this linear combination comes from observing azimuthal
dependence of the HE.sub.l+1,m.sup.even and HE.sub.l+1,m.sup.odd modes
comprising cos(.phi.) and sin (.phi.). If we denote the electric field of
HE.sub.l+1,m.sup.even and HE.sub.l+1,m.sup.odd modes as e.sub.1 and
e.sub.2, respectively, and similarly, denote their magnetic fields as
h.sub.1 and h.sub.2, the expression for this new mode can be written as:
e=e.sub.1ie.sub.2, (2.35)
h=h.sub.1+ih.sub.2. (2.36)
then we derive:
e r = e i ( l + 1 ) .PHI. F l ( R )
##EQU00054## h z = e i ( l + 1 ) .PHI. n co (
.epsilon. 0 .mu. 0 ) 1 2 ( 2 .DELTA. ) 1 2 V
G l  ##EQU00054.2## e z = i e i ( l + 1 )
.PHI. ( 2 .DELTA. ) 1 2 V G l  ##EQU00054.3## h
r =  i e i ( l + 1 ) .PHI. n co (
.epsilon. 0 .mu. 0 ) 1 2 F l ( R ) ##EQU00054.4##
Where F.sub.l(R) is the Bessel function and
G l .+. = dF l dR .+. l R F l ##EQU00055##
[0233] We note that all the quantities have e.sup.i(l+1).phi. dependence
that indicates these modes might have OAM, similarly to the free space
case. Therefore the azimuthal and the longitudinal component of the
Poynting vector are:
S .PHI. =  n co ( .epsilon. 0 .mu. 0 ) 1 2
( 2 .DELTA. ) 1 2 V Re { F l * G l  }
##EQU00056## S z = n co ( .epsilon. 0 .mu. 0 ) 1 2
F l 2 ##EQU00056.2##
[0234] The ratio of the angular momentum flux to the energy flux therefore
becomes:
.0. M .0. W = l + 1 .omega. ##EQU00057##
[0235] We note that in the freespace case, this ratio is similar:
.0. M .0. W = .sigma. + 1 .omega. ##EQU00058##
where .sigma. represents the polarization of the beam and is bounded to
be 1<.sigma.<1. In our case, it can be easily shown that SAM of
the V.sup.+ state, is 1, leading to important conclusion that the OAM of
the V.sup.+lm state is l. Hence, this shows that, in an ideal fiber, OAM
mode exists.
[0236] Thus, since an orbital angular momentum mode may be detected within
the ideal fiber, it is possible to encode information using this OAM mode
in order to transmit different types of information having different
orbital angular momentums within the same optical wavelength.
[0237] The above description with respect to optical fiber assumed an
ideal scenario of perfectly symmetrical fibers having no longitudinal
changes within the fiber profile. Within real world fibers, random
perturbations can induce coupling between spatial and/or polarization
modes, causing propagating fields to evolve randomly through the fiber.
The random perturbations can be divided into two classes, as illustrated
in FIG. 43. Within the random perturbations 4302, the first class
comprises extrinsic perturbations 4304. Extrinsic perturbations 4304
include static and dynamic fluctuations throughout the longitudinal
direction of the fiber, such as the density and concentration
fluctuations natural to random glassy polymer materials that are included
within fibers. The second class includes extrinsic variations 4306 such
as microscopic random bends caused by stress, diameter variations, and
fiber core defects such as microvoids, cracks, or dust particles.
[0238] Mode coupling can be described by field coupling modes which
account for complex valued modal electric field amplitudes, or by power
coupling modes, which is a simplified description that accounts only for
real value modal powers. Early multimode fiber systems used incoherent
light emitting diode sources and power coupling models were widely used
to describe several properties including steady state, modal power
distributions, and fiber impulse responses. While recent multimode fiber
systems use coherent sources, power coupling modes are still used to
describe effects such as reduced differential group delays and plastic
multimode fibers.
[0239] By contrast, single mode fiber systems have been using laser
sources. The study of random birefringence and mode coupling in single
mode fibers which leads to polarization mode dispersion (PMD), uses field
coupling modes which predict the existence of principal states of
polarization (PSPs). PSPs are polarization states shown to undergo
minimal dispersion and are used for optical compensation of polarization
mode dispersion in direct detection single mode fiber systems. In recent
years, field coupling modes have been applied to multimode fibers,
predicting principal mode which are the basis for optical compensation of
modal dispersion in direct detection multimode fiber systems.
[0240] Mode coupling can be classified as weak or strong, depending on
whether the total system length of the optical fiber is comparable to, or
much longer than, a length scale over which propagating fields remain
correlated. Depending on the detection format, communication systems can
be divided into direct and coherent detection systems. In direct
detection systems, mode coupling must either be avoided by careful design
of fibers and modal D (multiplexers) and/or mitigated by adaptive optical
signal processing. In systems using coherent detection, any linear cross
talk between modes can be compensated by multiple input multiple output
(MIMO) digital signal processing (DSP), as previously discussed, but DSP
complexity increases with an increasing number of modes.
[0241] Referring now to FIG. 44, there were illustrated the intensity
patterns of the first order mode group within a vortex fiber. Arrows 4402
within the illustration show the polarization of the electric field
within the fiber. The top row illustrates vector modes that are the exact
vector solutions, and the bottom row shows the resultant, unstable LP11
modes commonly obtained at a fiber output. Specific linear combinations
of pairs of top row modes resulting in the variety of LP11 modes obtained
at the fiber output. Coupled mode 4402 is provided by the coupled pair of
mode 4404 and 4406. Coupled mode 4404 is provided by the coupled pair of
mode 4404 and mode 4408. Coupled mode 4416 is provided by the coupled
pair of mode 4406 and mode 4410, and coupled mode 4418 is provided by the
coupled pair of mode 4408 and mode 4410.
[0242] Typically, index separation of two polarizations and single mode
fibers is on the order of 107. While this small separation lowers the
PMD of the fiber, external perturbations can easily couple one mode into
another, and indeed in a single mode fiber, arbitrary polarizations are
typically observed at the output. Simple fiber polarization controller
that uses stress induced birefringence can be used to achieve any desired
polarization at the output of the fiber.
[0243] By the origin, mode coupling can be classified as distributed
(caused by random perturbations in fibers), or discrete (caused at the
modal couplers and the multiplexers). Most importantly, it has been shown
that small, effective index separation among higher order modes is the
main reason for mode coupling and mode instabilities. In particular, the
distributed mode coupling has been shown to be inversely proportional to
.DELTA.P with P greater than 4, depending on coupling conditions. Modes
within one group are degenerate. For this reason, in most multimode fiber
modes that are observed in the fiber output are in fact the linear
combinations of vector modes and are linearly polarized states. Hence,
optical angular momentum modes that are the linear combination of the HE
even, odd modes cannot coexist in these fibers due to coupling to
degenerate TE01 and TM01 states.
[0244] Thus, the combination of the various OAM modes is not likely to
generate modal coupling within the optical systems and by increasing the
number of OAM modes, the reduction in mode coupling is further benefited.
[0245] Referring now to FIGS. 45A and 45B, there is illustrated the
benefit of effective index separation in first order modes. FIG. 45A
illustrates a typical step index multimode fiber that does not exhibit
effective index separation causing mode coupling. The mode TM.sub.01
HE.sup.even.sub.21, mode HE.sup.odd.sub.21, and mode TE.sub.01 have
little effective index separation, and these modes would be coupled
together. Mode HE.sup.x,1.sub.11 has an effective index separation such
that this mode is not coupled with these other modes.
[0246] This can be compared with the same modes in FIG. 45B. In this case,
there is an effective separation 4502 between the TM.sub.01 mode and the
HE.sup.even.sub.21 mode and the TE.sub.01 mode and the HE.sup.odd.sub.21
mode. This effective separation causes no mode coupling between these
mode levels in a similar manner that was done in the same modes in FIG.
45A.
[0247] In addition to effective index separation, mode coupling also
depends on the strength of perturbation. An increase in the cladding
diameter of an optical fiber can reduce the bend induced perturbations in
the fiber. Special fiber design that includes the trench region can
achieve socalled bend insensitivity, which is predominant in fiber to
the home. Fiber design that demonstrates reduced bends and sensitivity of
higher order Bessel modes for high power lasers have been demonstrated.
Most important, a special fiber design can remove the degeneracy of the
first order mode, thus reducing the mode coupling and enabling the OAM
modes to propagate within these fibers.
[0248] Topological charge may be multiplexed to the wave length for either
linear or circular polarization. In the case of linear polarizations,
topological charge would be multiplexed on vertical and horizontal
polarization. In case of circular polarization, topological charge would
be multiplexed on left hand and right hand circular polarization.
[0249] The topological charges can be created using Spiral Phase Plates
(SPPs) such as that illustrated in FIG. 11E, phase mask holograms or a
Spatial Light Modulator (SLM) by adjusting the voltages on SLM which
creates properly varying index of refraction resulting in twisting of the
beam with a specific topological charge. Different topological charges
can be created and muxed together and demuxed to separate charges.
[0250] As Spiral Phase plates can transform a plane wave (l=0) to a
twisted wave of a specific helicity (i.e. l=+1), Quarter Wave Plates
(QWP) can transform a linear polarization (s=0) to circular polarization
(i.e. s=+1).
[0251] Cross talk and multipath interference can be reduced using
MultipleInputMultipleOutput (MIMO).
[0252] Most of the channel impairments can be detected using a control or
pilot channel and be corrected using algorithmic techniques (closed loop
control system).
Free Space Communications
[0253] An additional configuration in which the optical angular momentum
processing and multilayer overlay modulation technique described herein
above may prove useful within the optical network framework is use with
freespace optics communications. Freespace optics systems provide a
number of advantages over traditional UHF RF based systems from improved
isolation between the systems, the size and the cost of the
receivers/transmitters, lack of RF licensing laws, and by combining
space, lighting, and communication into the same system. Referring now to
FIG. 46, there is illustrated an example of the operation of a freespace
communication system. The freespace communication system utilizes a
freespace optics transmitter 4602 that transmits a light beam 4604 to a
freespace optics receiver 4606. The major difference between a
fiberoptic network and a freespace optic network is that the
information beam is transmitted through free space rather than over a
fiberoptic cable. This causes a number of link difficulties, which will
be more fully discussed herein below. Freespace optics is a line of
sight technology that uses the invisible beams of light to provide
optical bandwidth connections that can send and receive up to 2.5 Gbps of
data, voice, and video communications between a transmitter 4602 and a
receiver 4606. Freespace optics uses the same concepts as fiberoptics,
except without the use of a fiberoptic cable. Freespace optics systems
provide the light beam 4604 within the infrared (IR) spectrum, which is
at the low end of the light spectrum. Specifically, the optical signal is
in the range of 300 Gigahertz to 1 Terahertz in terms of wavelength.
[0254] Presently existing freespace optics systems can provide data rates
of up to 10 Gigabits per second at a distance of up to 2.5 kilometers. In
outer space, the communications range of free space optical
communications is currently on the order of several thousand kilometers,
but has the potential to bridge interplanetary distances of millions of
kilometers, using optical telescopes as beam expanders. In January of
2013, NASA used lasers to beam an image of the Mona Lisa to the Lunar
Reconnaissance Orbiter roughly 240,000 miles away. To compensate for
atmospheric interference, an error correction code algorithm, similar to
that used within compact discs, was implemented.
[0255] The distance records for optical communications involve detection
and emission of laser light by space probes. A twoway distance record
for communication was established by the Mercury Laser Altimeter
instrument aboard the MESSENGER spacecraft. This infrared diode neodymium
laser, designed as a laser altimeter for a Mercury Orbiter mission, was
able to communicate across a distance of roughly 15,000,000 miles
(24,000,000 kilometers) as the craft neared Earth on a fly by in May of
2005. The previous record had been set with a oneway detection of laser
light from Earth by the Galileo Probe as two ground based lasers were
seen from 6,000,000 kilometers by the outbound probe in 1992. Researchers
used a white LED based space lighting system for indoor local area
network communications.
[0256] Referring now to FIG. 47, there is illustrated a block diagram of a
freespace optics system using orbital angular momentum and multilevel
overlay modulation according to the present disclosure. The OAM twisted
signals, in addition to being transmitted over fiber, may also be
transmitted using free optics. In this case, the transmission signals are
generated within transmission circuitry 4702 at each of the FSO
transceivers 4704. Freespace optics technology is based on the
connectivity between the FSO based optical wireless units, each
consisting of an optical transceiver 4704 with a transmitter 4702 and a
receiver 4706 to provide full duplex open pair and bidirectional closed
pairing capability. Each optical wireless transceiver unit 4704
additionally includes an optical source 4708 plus a lens or telescope
4710 for transmitting light through the atmosphere to another lens 4710
receiving the information. At this point, the receiving lens or telescope
4710 connects to a high sensitivity receiver 4706 via optical fiber 4712.
The transmitting transceiver 4704a and the receiving transceiver 4704b
have to have line of sight to each other. Trees, buildings, animals, and
atmospheric conditions all can hinder the line of sight needed for this
communications medium. Since line of sight is so critical, some systems
make use of beam divergence or a diffused beam approach, which involves a
large field of view that tolerates substantial line of sight interference
without significant impact on overall signal quality. The system may also
be equipped with auto tracking mechanism 4714 that maintains a tightly
focused beam on the receiving transceiver 3404b, even when the
transceivers are mounted on tall buildings or other structures that sway.
[0257] The modulated light source used with optical source 4708 is
typically a laser or light emitting diode (LED) providing the transmitted
optical signal that determines all the transmitter capabilities of the
system. Only the detector sensitivity within the receiver 4706 plays an
equally important role in total system performance. For
telecommunications purposes, only lasers that are capable of being
modulated at 20 Megabits per second to 2.5 Gigabits per second can meet
current marketplace demands. Additionally, how the device is modulated
and how much modulated power is produced are both important to the
selection of the device. Lasers in the 780850 nm and 15201600 nm
spectral bands meet frequency requirements.
[0258] Commercially available FSO systems operate in the near IR
wavelength range between 750 and 1600 nm, with one or two systems being
developed to operate at the IR wavelength of 10,000 nm. The physics and
transmissions properties of optical energy as it travels through the
atmosphere are similar throughout the visible and near IR wavelength
range, but several factors that influence which wavelengths are chosen
for a particular system.
[0259] The atmosphere is considered to be highly transparent in the
visible and near IR wavelength. However, certain wavelengths or
wavelength bands can experience severe absorption. In the near IR
wavelength, absorption occurs primarily in response to water particles
(i.e., moisture) which are an inherent part of the atmosphere, even under
clear weather conditions. There are several transmission windows that are
nearly transparent (i.e., have an attenuation of less than 0.2 dB per
kilometer) within the 70010,000 nm wavelength range. These wavelengths
are located around specific center wavelengths, with the majority of
freespace optics systems designed to operate in the windows of 780850
nm and 15201600 nm.
[0260] Wavelengths in the 780850 nm range are suitable for freespace
optics operation and higher power laser sources may operate in this
range. At 780 nm, inexpensive CD lasers may be used, but the average
lifespan of these lasers can be an issue. These issues may be addressed
by running the lasers at a fraction of their maximum rated output power
which will greatly increase their lifespan. At around 850 nm, the optical
source 4708 may comprise an inexpensive, high performance transmitter and
detector components that are readily available and commonly used in
network transmission equipment. Highly sensitive silicon (SI) avalanche
photodiodes (APD) detector technology and advanced vertical cavity
emitting laser may be utilized within the optical source 4708.
[0261] VCSEL technology may be used for operation in the 780 to 850 nm
range. Possible disadvantage of this technology include beam detection
through the use of a night vision scope, although it is still not
possible to demodulate a perceived light beam using this technique.
[0262] Wavelengths in the 15201600 nm range are wellsuited for
freespace transmission, and high quality transmitter and detector
components are readily available for use within the optical source block
4708. The combination of low attenuation and high component availability
within this wavelength range makes the development of wavelength division
multiplexing (WDM) freespace optics systems feasible. However,
components are generally more expensive and detectors are typically less
sensitive and have a smaller receive surface area when compared with
silicon avalanche photodiode detectors that operator at the 850 nm
wavelength. These wavelengths are compatible with erbiumdoped fiber
amplifier technology, which is important for high power (greater than 500
milliwatt) and high data rate (greater than 2.5 Gigabytes per second)
systems. Fifty to 65 times as much power can be transmitted at the
15201600 nm wavelength than can be transmitted at the 780850 nm
wavelength for the same eye safety classification. Disadvantages of these
wavelengths include the inability to detect a beam with a night vision
scope. The night vision scope is one technique that may be used for
aligning the beam through the alignment circuitry 4714. Class 1 lasers
are safe under reasonably foreseeable operating conditions including the
use of optical instruments for intrabeam viewing. Class 1 systems can be
installed at any location without restriction.
[0263] Another potential optical source 4708 comprised Class 1M lasers.
Class 1M laser systems operate in the wavelength range from 302.5 to 4000
nm, which is safe under reasonably foreseeable conditions, but may be
hazardous if the user employs optical instruments within some portion of
the beam path. As a result, Class 1M systems should only be installed in
locations where the unsafe use of optical aids can be prevented. Examples
of various characteristics of both Class 1 and Class 1M lasers that may
be used for the optical source 4708 are illustrated in Table G below.
TABLEUS00007
TABLE G
Laser Power Aperture Size Distance Power Density
Classification (mW) (mm) (m) (mW/cm.sup.2)
850nm Wavelength
Class 1 0.78 7 14 2.03
50 2000 0.04
Class 1M 0.78 7 100 2.03
500 7 14 1299.88
50 2000 25.48
1550nm Wavelength
Class 1 10 7 14 26.00
25 2000 2.04
Class 1M 10 3.5 100 103.99
500 7 14 1299.88
25 2000 101.91
[0264] The 10,000 nm wavelength is relatively new to the commercial free
space optic arena and is being developed because of better fog
transmission capabilities. There is presently considerable debate
regarding these characteristics because they are heavily dependent upon
fog type and duration. Few components are available at the 10,000 nm
wavelength, as it is normally not used within telecommunications
equipment. Additionally, 10,000 nm energy does not penetrate glass, so it
is illsuited to behind window deployment.
[0265] Within these wavelength windows, FSO systems should have the
following characteristics. The system should have the ability to operate
at higher power levels, which is important for longer distance FSO system
transmissions. The system should have the ability to provide high speed
modulation, which is important for high speed FSO systems. The system
should provide a small footprint and low power consumption, which is
important for overall system design and maintenance. The system should
have the ability to operate over a wide temperature range without major
performance degradations such that the systems may prove useful for
outdoor systems. Additionally, the mean time between failures should
exceed 10 years. Presently existing FSO systems generally use VCSELS for
operation in the shorter IR wavelength range, and FabryPerot or
distributed feedback lasers for operation in the longer IR wavelength
range. Several other laser types are suitable for high performance FSO
systems.
[0266] A freespace optics system using orbital angular momentum
processing and multilayer overlay modulation would provide a number of
advantages. The system would be very convenient. Freespace optics
provides a wireless solution to a lastmile connection, or a connection
between two buildings. There is no necessity to dig or bury fiber cable.
Freespace optics also requires no RF license. The system is upgradable
and its open interfaces support equipment from a variety of vendors. The
system can be deployed behind windows, eliminating the need for costly
rooftop right. It is also immune to radiofrequency interference or
saturation. The system is also fairly speedy. The system provides 2.5
Gigabits per second of data throughput. This provides ample bandwidth to
transfer files between two sites. With the growth in the size of files,
freespace optics provides the necessary bandwidth to transfer these
files efficiently.
[0267] Freespace optics also provides a secure wireless solution. The
laser beam cannot be detected with a spectral analyzer or RF meter. The
beam is invisible, which makes it difficult to find. The laser beam that
is used to transmit and receive the data is very narrow. This means that
it is almost impossible to intercept the data being transmitted. One
would have to be within the line of sight between the receiver and the
transmitter in order to be able to accomplish this feat. If this occurs,
this would alert the receiving site that a connection has been lost.
Thus, minimal security upgrades would be required for a freespace optics
system.
[0268] However, there are several weaknesses with freespace optics
systems. The distance of a freespace optics system is very limited.
Currently operating distances are approximately within 2 kilometers.
Although this is a powerful system with great throughput, the limitation
of distance is a big deterrent for fullscale implementation.
Additionally, all systems require line of sight be maintained at all
times during transmission. Any obstacle, be it environmental or animals
can hinder the transmission. Freespace optic technology must be designed
to combat changes in the atmosphere which can affect freespace optic
system performance capacity.
[0269] Something that may affect a freespace optics system is fog. Dense
fog is a primary challenge to the operation of freespace optics systems.
Rain and snow have little effect on freespace optics technology, but fog
is different. Fog is a vapor composed of water droplets which are only a
few hundred microns in diameter, but can modify light characteristics or
completely hinder the passage of light through a combination of
absorption, scattering, and reflection. The primary answer to counter fog
when deploying freespace optic based wireless products is through a
network design that shortens FSO linked distances and adds network
redundancies.
[0270] Absorption is another problem. Absorption occurs when suspended
water molecules in the terrestrial atmosphere extinguish photons. This
causes a decrease in the power density (attenuation) of the free space
optics beam and directly affects the availability of the system.
Absorption occurs more readily at some wavelengths than others. However,
the use of appropriate power based on atmospheric conditions and the use
of spatial diversity (multiple beams within an FSO based unit), helps
maintain the required level of network availability.
[0271] Solar interference is also a problem. Freespace optics systems use
a high sensitivity receiver in combination with a larger aperture lens.
As a result, natural background light can potentially interfere with
freespace optics signal reception. This is especially the case with the
high levels of background radiation associated with intense sunlight. In
some instances, direct sunlight may case link outages for periods of
several minutes when the sun is within the receiver's field of vision.
However, the times when the receiver is most susceptible to the effects
of direct solar illumination can be easily predicted. When direct
exposure of the equipment cannot be avoided, the narrowing of receiver
field of vision and/or using narrow bandwidth light filters can improve
system performance. Interference caused by sunlight reflecting off of a
glass surface is also possible.
[0272] Scattering issues may also affect connection availability.
Scattering is caused when the wavelength collides with the scatterer. The
physical size of the scatterer determines the type of scattering. When
the scatterer is smaller than the wavelength, this is known as Rayleigh
scattering. When a scatterer is of comparable size to the wavelengths,
this is known as Mie scattering. When the scattering is much larger than
the wavelength, this is known as nonselective scattering. In scattering,
unlike absorption, there is no loss of energy, only a directional
redistribution of energy that may have significant reduction in beam
intensity over longer distances.
[0273] Physical obstructions such as flying birds or construction cranes
can also temporarily block a single beam free space optics system, but
this tends to cause only short interruptions. Transmissions are easily
and automatically resumed when the obstacle moves. Optical wireless
products use multibeams (spatial diversity) to address temporary
abstractions as well as other atmospheric conditions, to provide for
greater availability.
[0274] The movement of buildings can upset receiver and transmitter
alignment. Freespace optics based optical wireless offerings use
divergent beams to maintain connectivity. When combined with tracking
mechanisms, multiple beam FSO based systems provide even greater
performance and enhanced installation simplicity.
[0275] Scintillation is caused by heated air rising from the Earth or
manmade devices such as heating ducts that create temperature variations
among different pockets of air. This can cause fluctuations in signal
amplitude, which leads to "image dancing" at the freespace optics based
receiver end. The effects of this scintillation are called "refractive
turbulence." This causes primarily two effects on the optical beams. Beam
wander is caused by the turbulent eddies that are no larger than the
beam. Beam spreading is the spread of an optical beam as it propagates
through the atmosphere.
[0276] Referring now to FIGS. 48A through 48D, in order to achieve higher
data capacity within optical links, an additional degree of freedom from
multiplexing multiple data channels must be exploited. Moreover, the
ability to use two different orthogonal multiplexing techniques together
has the potential to dramatically enhance system performance and
increased bandwidth.
[0277] One multiplexing technique which may exploit the possibilities is
mode division multiplexing (MDM) using orbital angular momentum (OAM).
OAM mode refers to laser beams within a freespace optical system or
fiberoptic system that have a phase term of e.sup.il.phi. in their wave
fronts, in which .phi. is the azimuth angle and l determines the OAM
value (topological charge). In general, OAM modes have a "donutlike"
ring shaped intensity distribution. Multiple spatial collocated laser
beams, which carry different OAM values, are orthogonal to each other and
can be used to transmit multiple independent data channels on the same
wavelength. Consequently, the system capacity and spectral efficiency in
terms of bits/S/Hz can be dramatically increased. Freespace
communications links using OAM may support 100 Tbits/capacity. Various
techniques for implementing this as illustrated in FIGS. 48A through 48D
include a combination of multiple beams 4802 having multiple different
OAM values 4804 on each wavelength. Thus, beam 4802 includes OAM values,
OAM1 and OAM4. Beam 4806 includes OAM value 2 and OAM value 5. Finally,
beam 4808 includes OAM3 value and OAM6 value. Referring now to FIG. 48B,
there is illustrated a single beam wavelength 4810 using a first group of
OAM values 4812 having both a positive OAM value 4812 and a negative OAM
value 4814. Similarly, OAM2 value may have a positive value 4816 and a
negative value 4818 on the same wavelength 4810.
[0278] FIG. 48C illustrates the use of a wavelength 4820 having
polarization multiplexing of OAM value. The wavelength 4820 can have
multiple OAM values 4822 multiplexed thereon. The number of available
channels can be further increased by applying left or right handed
polarization to the OAM values. Finally, FIG. 48D illustrates two groups
of concentric rings 4860, 4862 for a wavelength having multiple OAM
values.
[0279] Wavelength distribution multiplexing (WDM) has been widely used to
improve the optical communication capacity within both fiberoptic
systems and freespace communication system. OAM mode multiplexing and
WDM are mutually orthogonal such that they can be combined to achieve a
dramatic increase in system capacity. Referring now to FIG. 49, there is
illustrated a scenario where each WDM channel 4902 contains many
orthogonal OAM beam 4904. Thus, using a combination of orbital angular
momentum with wave division multiplexing, a significant enhancement in
communication link to capacity may be achieved.
[0280] Current optical communication architectures have considerable
routing challenges. A routing protocol for use with freespace optic
system must take into account the line of sight requirements for optical
communications within a freespace optics system. Thus, a freespace
optics network must be modeled as a directed hierarchical random sector
geometric graph in which sensors route their data via multihop paths to
a base station through a cluster head. This is a new efficient routing
algorithm for local neighborhood discovery and a base station uplink and
downlink discovery algorithm. The routing protocol requires order O
log(n) storage at each node versus order O(n) used within current
techniques and architectures.
[0281] Current routing protocols are based on link state, distance
vectors, path vectors, or source routing, and they differ from the new
routing technique in significant manners. First, current techniques
assume that a fraction of the links are bidirectional. This is not true
within a freespace optic network in which all links are unidirectional.
Second, many current protocols are designed for ad hoc networks in which
the routing protocol is designed to support multihop communications
between any pair of nodes. The goal of the sensor network is to route
sensor readings to the base station. Therefore, the dominant traffic
patterns are different from those in an ad hoc network. In a sensor
network, node to base stations, base station to nodes, and local
neighborhood communication are mostly used.
[0282] Recent studies have considered the effect of unidirectional links
and report that as many as 5 percent to 10 percent of links and wireless
ad hoc networks are unidirectional due to various factors. Routing
protocols such as DSDV and AODV use a reverse path technique, implicitly
ignoring such unidirectional links and are therefore not relevant in this
scenario. Other protocols such as DSR, ZRP, or ZRL have been designed or
modified to accommodate unidirectionality by detecting unidirectional
links and then providing bidirectional abstraction for such links.
Referring now to FIG. 50, the simplest and most efficient solution for
dealing with unidirectionality is tunneling, in which bidirectionality is
emulated for a unidirectional link by using bidirectional links on a
reverse back channel to establish the tunnel. Tunneling also prevents
implosion of acknowledgement packets and looping by simply pressing link
layer acknowledgements for tunneled packets received on a unidirectional
link. Tunneling, however, works well in mostly bidirectional networks
with few unidirectional links.
[0283] Within a network using only unidirectional links such as a
freespace optical network, systems such as that illustrated in FIGS. 50
and 51 would be more applicable. Nodes within a unidirectional network
utilize a directional transmit 5002 transmitting from the node 5000 in a
single, defined direction. Additionally, each node 5000 includes an
omnidirectional receiver 5004 which can receive a signal coming to the
node in any direction. Also, as discussed here and above, the node 5000
would also include a 0 log(n) storage 5006. Thus, each node 5000 provide
only unidirectional communications links. Thus, a series of nodes 5000 as
illustrated in FIG. 51 may unidirectionally communicate with any other
node 5000 and forward communication from one desk location to another
through a sequence of interconnected nodes.
[0284] Topological charge may be multiplexed to the wave length for either
linear or circular polarization. In the case of linear polarizations,
topological charge would be multiplexed on vertical and horizontal
polarization. In case of circular polarization, topological charge would
be multiplexed on left hand and right hand circular polarizations.
[0285] The topological charges can be created using Spiral Phase Plates
(SPPs) such as that illustrated in FIG. 11E, phase mask holograms or a
Spatial Light Modulator (SLM) by adjusting the voltages on SLM which
creates properly varying index of refraction resulting in twisting of the
beam with a specific topological charge. Different topological charges
can be created and muxed together and demuxed to separate charges.
[0286] As Spiral Phase plates can transform a plane wave (l=0) to a
twisted wave of a specific helicity (i.e. l=+1), Quarter Wave Plates
(QWP) can transform a linear polarization (s=0) to circular polarization
(i.e. s=+1).
[0287] Cross talk and multipath interference can be reduced using
MultipleInputMultipleOutput (MIMO).
[0288] Most of the channel impairments can be detected using a control or
pilot channel and be corrected using algorithmic techniques (closed loop
control system).
[0289] Multiplexing of the topological charge to the RF as well as free
space optics in real time provides redundancy and better capacity. When
channel impairments from atmospheric disturbances or scintillation impact
the information signals, it is possible to toggle between free space
optics to RF and back in real time. This approach still uses twisted
waves on both the free space optics as well as the RF signal. Most of the
channel impairments can be detected using a control or pilot channel and
be corrected using algorithmic techniques (closed loop control system) or
by toggling between the RF and free space optics.
[0290] In a further embodiment illustrated in FIG. 52, both RF signals and
free space optics may be implemented within a dual RF and free space
optics mechanism 5202. The dual RF and free space optics mechanism 5202
include a free space optics projection portion 5204 that transmits a
light wave having an orbital angular momentum applied thereto with
multilevel overlay modulation and a RF portion 5206 including circuitry
necessary for transmitting information with orbital angular momentum and
multilayer overlay on an RF signal 5210. The dual RF and free space
optics mechanism 5202 may be multiplexed in real time between the free
space optics signal 5208 and the RF signal 5210 depending upon operating
conditions. In some situations, the free space optics signal 5208 would
be most appropriate for transmitting the data. In other situations, the
free space optics signal 5208 would not be available and the RF signal
5210 would be most appropriate for transmitting data. The dual RF and
free space optics mechanism 5202 may multiplex in real time between these
two signals based upon the available operating conditions.
[0291] Multiplexing of the topological charge to the RF as well as free
space optics in real time provides redundancy and better capacity. When
channel impairments from atmospheric disturbances or scintillation impact
the information signals, it is possible to toggle between free space
optics to RF and back in real time. This approach still uses twisted
waves on both the free space optics as well as the RF signal. Most of the
channel impairments can be detected using a control or pilot channel and
be corrected using algorithmic techniques (closed loop control system) or
by toggling between the RF and free space optics.
Quantum Key Distribution
[0292] Referring now to FIG. 53, there is illustrated a further
improvement of a system utilizing orbital angular momentum processing. In
the illustration of FIG. 53, a transmitter 5302 and receiver 5304 are
interconnected over an optical link 5306. The optical link 5306 may
comprise a fiberoptic link or a freespace optic link as described
herein above. The transmitter receives a data stream 5308 that is
processed via orbital angular momentum processing circuitry 5310. The
orbital angular momentum processing circuitry 5310 provide orbital
angular momentum twist to various signals on separate channels as
described herein above. In some embodiments, the orbital angular momentum
processing circuitry may further provide multilayer overlay modulation
to the signal channels in order to further increase system bandwidth.
[0293] The OAM processed signals are provided to quantum key distribution
processing circuitry 5312. The quantum key distribution processing
circuitry 5312 utilizes the principals of quantum key distribution as
will be more fully described herein below to enable encryption of the
signal being transmitted over the optical link 5306 to the receiver 5304.
The received signals are processed within the receiver 5304 using the
quantum key distribution processing circuitry 5314. The quantum key
distribution processing circuitry 5314 decrypts the received signals
using the quantum key distribution processing as will be more fully
described herein below. The decrypted signals are provided to orbital
angular momentum processing circuitry 5316 which removes any orbital
angular momentum twist from the signals to generate the plurality of
output signals 5318. As mentioned previously, the orbital angular
momentum processing circuitry 5316 may also demodulate the signals using
multilayer overlay modulation included within the received signals.
[0294] Orbital angular momentum in combination with optical polarization
is exploited within the circuit of FIG. 53 in order to encode information
in rotation invariant photonic states, so as to guarantee full
independence of the communication from the local reference frames of the
transmitting unit 5302 and the receiving unit 5304. There are various
ways to implement quantum key distribution (QKD), a protocol that
exploits the features of quantum mechanics to guarantee unconditional
security in cryptographic communications with error rate performances
that are fully compatible with real world application environments.
[0295] Encrypted communication requires the exchange of keys in a
protected manner. This key exchanged is often done through a trusted
authority. Quantum key distribution is an alternative solution to the key
establishment problem. In contrast to, for example, public key
cryptography, quantum key distribution has been proven to be
unconditionally secure, i.e., secure against any attack, even in the
future, irrespective of the computing power or in any other resources
that may be used. Quantum key distribution security relies on the laws of
quantum mechanics, and more specifically on the fact that it is
impossible to gain information about nonorthogonal quantum states
without perturbing these states. This property can be used to establish
random keys between a transmitter and receiver, and guarantee that the
key is perfectly secret from any third party eavesdropping on the line.
[0296] In parallel to the "full quantum proofs" mentioned above, the
security of QKD systems has been put on stable information theoretic
footing, thanks to the work on secret key agreements done in the
framework of information theoretic cryptography and to its extensions,
triggered by the new possibilities offered by quantum information.
Referring now to FIG. 54, within a basic QKD system, a QKD link 5402 is a
point to point connection between a transmitter 5404 and a receiver 5406
that want to share secret keys. The QKD link 5402 is constituted by the
combination of a quantum channel 5408 and a classic channel 5410. The
transmitter 5404 generates a random stream of classical bits and encodes
them into a sequence of nonorthogonal states of light that are
transmitted over the quantum channel 5408. Upon reception of these
quantum states, the receiver 5406 performs some appropriate measurements
leading the receiver to share some classical data over the classical link
5410 correlated with the transmitter bit stream. The classical channel
5410 is used to test these correlations.
[0297] If the correlations are high enough, this statistically implies
that no significant eavesdropping has occurred on the quantum channel
5408 and thus, that has a very high probability, a perfectly secure,
symmetric key can be distilled from the correlated data shared by the
transmitter 5404 and the receiver 5406. In the opposite case, the key
generation process has to be aborted and started again. The quantum key
distribution is a symmetric key distribution technique. Quantum key
distribution requires, for authentication purposes, that the transmitter
5404 and receiver 5406 share in advance a short key whose length scales
only logarithmically in the length of the secret key generated by an OKD
session.
[0298] Quantum key distribution on a regional scale has already been
demonstrated in a number of countries. However, freespace optical links
are required for long distance communication among areas which are not
suitable for fiber installation or for moving terminals, including the
important case of satellite based links. The present approach exploits
spatial transverse modes of the optical beam, in particular of the OAM
degree of freedom, in order to acquire a significant technical advantage
that is the insensitivity of the communication to relevant alignment of
the user's reference frames. This advantage may be very relevant for
quantum key distribution implementation to be upgraded from the regional
scale to a national or continental one, or for links crossing hostile
ground, and even for envisioning a quantum key distribution on a global
scale by exploiting orbiting terminals on a network of satellites.
[0299] The OAM Eigen modes are characterized by a twisted wavefront
composed of "l" intertwined helices, where "l" is an integer, and by
photons carrying ".+.l " of (orbital) angular momentum, in addition to
the more usual spin angular momentum (SAM) associated with polarization.
The potentially unlimited value of "l" opens the possibility to exploit
OAM also for increasing the capacity of communication systems (although
at the expense of increasing also the channel crosssection size), and
terabit classical data transmission based on OAM multiplexing can be
demonstrated both in freespace and optical fibers. Such a feature can
also be exploited in the quantum domain, for example to expand the number
of qubits per photon, or to achieve new functions, such as the rotational
invariance of the qubits.
[0300] In a freespace QKD, two users (Alice and Bob) must establish a
shared reference frame (SRF) in order to communicate with good fidelity.
Indeed the lack of a SRF is equivalent to an unknown relative rotation
which introduces noise into the quantum channel, disrupting the
communication. When the information is encoded in photon polarization,
such a reference frame can be defined by the orientations of Alice's and
Bob's "horizontal" linear polarization directions. The alignment of these
directions needs extra resources and can impose serious obstacles in long
distance free space QKD and/or when the misalignment varies in time. As
indicated, we can solve this by using rotation invariant states, which
remove altogether the need for establishing a SRF. Such states are
obtained as a particular combination of OAM and polarization modes
(hybrid states), for which the transformation induced by the misalignment
on polarization is exactly balanced by the effect of the same
misalignment on spatial modes. These states exhibit a global symmetry
under rotations of the beam around its axis and can be visualized as
spacevariant polarization states, generalizing the wellknown azimuthal
and radial vector beams, and forming a twodimensional Hilbert space.
Moreover, this rotationinvariant hybrid space can be also regarded as a
decoherencefree subspace of the fourdimensional OAMpolarization
product Hilbert space, insensitive to the noise associated with random
rotations.
[0301] The hybrid states can be generated by a particular spacevariant
birefringent plate having topological charge "q" at its center, named
"qplate". In particular, a polarized Gaussian beam (having zero OAM)
passing through a qplate with q=1/2 will undergo the following
transformation:
(.alpha.R+.beta.R).sub..pi.0.sub.0.fwdarw..alpha.L.sub..pi..gamma..
sub.0+.beta.R.sub..pi.l.sub.0
[0302] L>.sub..pi..sub._ and R>.sub..pi. denote the left and right
circular polarization states (eigenstates of SAM with eigenvalues
".+."), 0>.sub.O represents the transverse Gaussian mode with zero
OAM and the L>.sub.O.sub. and R>.sub.O eigenstates of OAM with
l=1 and with eigenvalues ".+.l "). The states appearing on the right
hand side of equation are rotationinvariant states. The reverse
operation to this can be realized by a second qplate with the same q. In
practice, the qplate operates as an interface between the polarization
space and the hybrid one, converting qubits from one space to the other
and vice versa in a universal (qubit invariant) way. This in turn means
that the initial encoding and final decoding of information in our QKD
implementation protocol can be conveniently performed in the polarization
space, while the transmission is done in the rotationinvariant hybrid
space.
[0303] OAM is a conserved quantity for light propagation in vacuum, which
is obviously important for communication applications. However, OAM is
also highly sensitive to atmospheric turbulence, a feature which limits
its potential usefulness in many practical cases unless new techniques
are developed to deal with such issues.
[0304] Quantum cryptography describes the use of quantum mechanical
effects (in particular quantum communication and quantum computation) to
perform cryptographic tasks or to break cryptographic systems. Wellknown
examples of quantum cryptography are the use of quantum communication to
exchange a key securely (quantum key distribution) and the hypothetical
use of quantum computers that would allow the breaking of various popular
publickey encryption and signature schemes (e.g., RSA).
[0305] The advantage of quantum cryptography lies in the fact that it
allows the completion of various cryptographic tasks that are proven to
be impossible using only classical (i.e. nonquantum) communication. For
example, quantum mechanics guarantees that measuring quantum data
disturbs that data; this can be used to detect eavesdropping in quantum
key distribution.
[0306] Quantum key distribution (QKD) uses quantum mechanics to guarantee
secure communication. It enables two parties to produce a shared random
secret key known only to them, which can then be used to encrypt and
decrypt messages.
[0307] An important and unique property of quantum distribution is the
ability of the two communicating users to detect the presence of any
third party trying to gain knowledge of the key. This results from a
fundamental aspect of quantum mechanics: the process of measuring a
quantum system in general disturbs the system. A third party trying to
eavesdrop on the key must in some way measure it, thus introducing
detectable anomalies. By using quantum superposition or quantum
entanglement and transmitting information in quantum states, a
communication system can be implemented which detects eavesdropping. If
the level of eavesdropping is below a certain threshold, a key can be
produced that is guaranteed to be secure (i.e. the eavesdropper has no
information about it), otherwise no secure key is possible and
communication is aborted.
[0308] The security of quantum key distribution relies on the foundations
of quantum mechanics, in contrast to traditional key distribution
protocol which relies on the computational difficulty of certain
mathematical functions, and cannot provide any indication of
eavesdropping or guarantee of key security.
[0309] Quantum key distribution is only used to reduce and distribute a
key, not to transmit any message data. This key can then be used with any
chosen encryption algorithm to encrypt (and decrypt) a message, which is
transmitted over a standard communications channel. The algorithm most
commonly associated with QKD is the onetime pad, as it is provably
secure when used with a secret, random key.
[0310] Quantum communication involves encoding information in quantum
states, or qubits, as opposed to classical communication's use of bits.
Usually, photons are used for these quantum states and thus is applicable
within optical communication systems. Quantum key distribution exploits
certain properties of these quantum states to ensure its security. There
are several approaches to quantum key distribution, but they can be
divided into two main categories, depending on which property they
exploit. The first of these are prepare and measure protocol. In contrast
to classical physics, the act of measurement is an integral part of
quantum mechanics. In general, measuring an unknown quantum state changes
that state in some way. This is known as quantum indeterminacy, and
underlies results such as the Heisenberg uncertainty principle,
information distribution theorem, and no cloning theorem. This can be
exploited in order to detect any eavesdropping on communication (which
necessarily involves measurement) and, more importantly, to calculate the
amount of information that has been intercepted. Thus, by detecting the
change within the signal, the amount of eavesdropping or information that
has been intercepted may be determined by the receiving party.
[0311] The second category involves the use of entanglement based
protocols. The quantum states of two or more separate objects can become
linked together in such a way that they must be described by a combined
quantum state, not as individual objects. This is known as entanglement,
and means that, for example, performing a measurement on one object
affects the other object. If an entanglement pair of objects is shared
between two parties, anyone intercepting either object alters the overall
system, revealing the presence of a third party (and the amount of
information that they have gained). Thus, again, undesired reception of
information may be determined by change in the entangled pair of objects
that is shared between the parties when intercepted by an unauthorized
third party.
[0312] One example of a quantum key distribution (QKD) protocol is the
BB84 protocol. The BB84 protocol was originally described using photon
polarization states to transmit information. However, any two pairs of
conjugate states can be used for the protocol, and optical fiberbased
implementations described as BB84 can use phaseencoded states. The
transmitter (traditionally referred to as Alice) and the receiver
(traditionally referred to as Bob) are connected by a quantum
communication channel which allows quantum states to be transmitted. In
the case of photons, this channel is generally either an optical fiber,
or simply freespace, as described previously with respect to FIG. 53. In
addition, the transmitter and receiver communicate via a public classical
channel, for example using broadcast radio or the Internet. Neither of
these channels needs to be secure. The protocol is designed with the
assumption that an eavesdropper (referred to as Eve) can interfere in any
way with both the transmitter and receiver.
[0313] Referring now to FIG. 55, the security of the protocol comes from
encoding the information in nonorthogonal states. Quantum indeterminacy
means that these states cannot generally be measured without disturbing
the original state. BB84 uses two pair of states 5502, each pair
conjugate to the other pair to form a conjugate pair 5504. The two states
5502 within a pair 5504 are orthogonal to each other. Pairs of orthogonal
states are referred to as a basis. The usual polarization state pairs
used are either the rectilinear basis of vertical (0 degrees) and
horizontal (90 degrees), the diagonal basis of 45 degrees and 135
degrees, or the circular basis of left handedness and/or right
handedness. Any two of these basis are conjugate to each other, and so
any two can be used in the protocol. In the example of FIG. 56,
rectilinear basis are used at 5602 and 5604, respectively, and diagonal
basis are used at 5606 and 5608.
[0314] The first step in BB84 protocol is quantum transmission. Referring
now to FIG. 57 wherein there is illustrated a flow diagram describing the
process, wherein the transmitter creates a random bit (0 or 1) at step
5702, and randomly selects at 5704 one of the two basis, either
rectilinear or diagonal, to transmit the random bit. The transmitter
prepares at step 5706 a photon polarization state depending both on the
bit value and the selected basis, as shown in FIG. 55. So, for example, a
0 is encoded in the rectilinear basis (+) as a vertical polarization
state and a 1 is encoded in a diagonal basis (X) as a 135 degree state.
The transmitter transmits at step 5708 a single proton in the state
specified to the receiver using the quantum channel. This process is
repeated from the random bit stage at step 5702 with the transmitter
recording the state, basis, and time of each photon that is sent over the
optical link.
[0315] According to quantum mechanics, no possible measurement
distinguishes between the four different polarization states 5602 through
5608 of FIG. 56, as they are not all orthogonal. The only possible
measurement is between any two orthogonal states (and orthonormal basis).
So, for example, measuring in the rectilinear basis gives a result of
horizontal or vertical. If the photo was created as horizontal or
vertical (as a rectilinear eigenstate), then this measures the correct
state, but if it was created as 45 degrees or 135 degrees (diagonal
eigenstate), the rectilinear measurement instead returns either
horizontal or vertical at random. Furthermore, after this measurement,
the proton is polarized in the state it was measured in (horizontal or
vertical), with all of the information about its initial polarization
lost.
[0316] Referring now to FIG. 58, as the receiver does not know the basis
the photons were encoded in, the receiver can only select a basis at
random to measure in, either rectilinear or diagonal. At step 5802, the
transmitter does this for each received photon, recording the time
measurement basis used and measurement result at step 5804. At step 5806,
a determination is made if there are further protons present and, if so,
control passes back to step 5802. Once inquiry step 5806 determines the
receiver had measured all of the protons, the transceiver communicates at
step 5808 with the transmitter over the public communications channel.
The transmitter broadcast the basis for each photon that was sent at step
5810 and the receiver broadcasts the basis each photon was measured in at
step 5812. Each of the transmitter and receiver discard photon
measurements where the receiver used a different basis at step 5814
which, on average, is onehalf, leaving half of the bits as a shared key,
at step 5816. This process is more fully illustrated in FIG. 59.
[0317] The transmitter transmits the random bit 01101001. For each of
these bits respectively, the transmitter selects the sending basis of
rectilinear, rectilinear, diagonal, rectilinear, diagonal, diagonal,
diagonal, and rectilinear. Thus, based upon the associated random bits
selected and the random sending basis associated with the signal, the
polarization indicated in line 5802 is provided. Upon receiving the
photon, the receiver selects the random measuring basis as indicated in
line 5904. The photon polarization measurements from these basis will
then be as indicated in line 5906. A public discussion of the transmitted
basis and the measurement basis are discussed at 5908 and the secret key
is determined to be 0101 at 5910 based upon the matching bases for
transmitted photons 1, 3, 6, and 8.
[0318] Referring now to FIG. 60, there is illustrated the process for
determining whether to keep or abort the determined key based upon errors
detected within the determined bit string. To check for the presence of
eavesdropping, the transmitter and receiver compare a certain subset of
their remaining bit strings at step 6002. If a third party has gained any
information about the photon's polarization, this introduces errors
within the receiver's measurements. If more than P bits differ at inquiry
step 6004, the key is aborted at step 6006, and the transmitter and
receiver try again, possibly with a different quantum channel, as the
security of the key cannot be guaranteed. P is chosen so that if the
number of bits that is known to the eavesdropper is less than this,
privacy amplification can be used to reduce the eavesdropper's knowledge
of the key to an arbitrarily small amount by reducing the length of the
key. If inquiry step 6004 determines that the number of bits is not
greater than P, then the key may be used at step 6008.
[0319] The E91 protocol comprises another quantum key distribution scheme
that uses entangled pairs of protons. The entangled pairs can be created
by the transmitter, by the receiver, or by some other source separate
from both of the transmitter and receiver, including an eavesdropper. The
photons are distributed so that the transmitter and receiver each end up
with one photon from each pair. The scheme relies on two properties of
entanglement. First, the entangled states are perfectly correlated in the
sense that if the transmitter and receiver both measure whether their
particles have vertical or horizontal polarizations, they always get the
same answer with 100 percent probability. The same is true if they both
measure any other pair of complementary (orthogonal) polarizations.
However, the particular results are not completely random. It is
impossible for the transmitter to predict if the transmitter, and thus
the receiver, will get vertical polarizations or horizontal
polarizations. Second, any attempt at eavesdropping by a third party
destroys these correlations in a way that the transmitter and receiver
can detect. The original Ekert protocol (E91) consists of three possible
states and testing Bell inequality violation for detecting eavesdropping.
[0320] Presently, the highest bit rate systems currently using quantum key
distribution demonstrate the exchange of secure keys at 1 Megabit per
second over a 20 kilometer optical fiber and 10 Kilobits per second over
a 100 kilometer fiber.
[0321] The longest distance over which quantum key distribution has been
demonstrated using optical fiber is 148 kilometers. The distance is long
enough for almost all of the spans found in today's fiberoptic networks.
The distance record for freespace quantum key distribution is 144
kilometers using BB84 enhanced with decoy states.
[0322] Referring now to FIG. 61, there is illustrated a functional block
diagram of a transmitter 6102 and receiver 6104 that can implement
alignment of freespace quantum key distribution. The system can
implement the BB84 protocol with decoy states. The controller 6106
enables the bits to be encoded in two mutually unbiased bases Z={0>,
1>} and X={+>, >}, where 0> and 1> are two
orthogonal states spanning the qubit space and .+.=1/ 2 (0.+.1). The
transmitter controller 6106 randomly chooses between the Z and X basis to
send the classical bits 0 and 1. Within hybrid encoding, the Z basis
corresponds to {L.sub..pi.r.sub.O, R.sub..pi.l.sub.O} while the X
basis states correspond to 1/ 2
(L.sub..pi.r.sub.O.+.R.sub..pi.l.sub.O). The transmitter 6102 uses
four different polarized attenuated lasers 6108 to generate quantum bits
through the quantum bit generator 6110. Photons from the quantum bit
generator 4610 are delivered via a single mode fiber 6112 to a telescope
6114. Polarization states H>, V>, R>, L> are transformed
into rotation invariant hybrid states by means of a qplate 6116 with
q=1/2. The photons can then be transmitted to the receiving station 6104
where a second qplate transform 6118 transforms the signals back into
the original polarization states H>, V>, R>, L>, as
defined by the receiver reference frame. Qubits can then be analyzed by
polarizers 6120 and single photon detectors 6122. The information from
the polarizers 6120 and photo detectors 6122 may then be provided to the
receiver controller 6124 such that the shifted keys can be obtained by
keeping only the bits corresponding to the same basis on the transmitter
and receiver side as determined by communications over a classic channel
between the transceivers 6126, 6128 in the transmitter 6102 and receiver
6104.
[0323] Referring now to FIG. 62, there is illustrated a network cloud
based quantum key distribution system including a central server 6202 and
various attached nodes 6204 in a hub and spoke configuration. Trends in
networking are presenting new security concerns that are challenging to
meet with conventional cryptography, owing to constrained computational
resources or the difficulty of providing suitable key management. In
principle, quantum cryptography, with its forward security and
lightweight computational footprint, could meet these challenges,
provided it could evolve from the current point to point architecture to
a form compatible with multimode network architecture. Trusted quantum
key distribution networks based on a mesh of point to point links lacks
scalability, require dedicated optical fibers, are expensive and not
amenable to mass production since they only provide one of the
cryptographic functions, namely key distribution needed for secure
communications. Thus, they have limited practical interest.
[0324] A new, scalable approach such as that illustrated in FIG. 62
provides quantum information assurance that is network based quantum
communications which can solve new network security challenges. In this
approach, a BB84 type quantum communication between each of N client
nodes 6204 and a central sever 6202 at the physical layer support a
quantum key management layer, which in turn enables secure communication
functions (confidentiality, authentication, and nonrepudiation) at the
application layer between approximately N2 client pairs. This network
based communication "hub and spoke" topology can be implemented in a
network setting, and permits a hierarchical trust architecture that
allows the server 6202 to act as a trusted authority in cryptographic
protocols for quantum authenticated key establishment. This avoids the
poor scaling of previous approaches that required a preexisting trust
relationship between every pair of nodes. By making a server 6202, a
single multiplex QC (quantum communications) receiver and the client
nodes 6204 QC transmitters, this network can simplify complexity across
multiple network nodes. In this way, the network based quantum key
distribution architecture is scalable in terms of both quantum physical
resources and trust. One can at time multiplex the server 6202 with three
transmitters 6204 over a single mode fiber, larger number of clients
could be accommodated with a combination of temporal and wavelength
multiplexing as well as orbital angular momentum multiplexed with wave
division multiplexing to support much higher clients.
[0325] Referring now to FIGS. 63 and 64, there are illustrated various
components of multiuser orbital angular momentum based quantum key
distribution multiaccess network. FIG. 63 illustrates a high speed
single photon detector 6302 positioned at a network node that can be
shared between multiple users 6304 using conventional network
architectures, thereby significantly reducing the hardware requirements
for each user added to the network. In an embodiment, the single photon
detector 6302 may share up to 64 users. This shared receiver architecture
removes one of the main obstacles restricting the widespread application
of quantum key distribution. The embodiment presents a viable method for
realizing multiuser quantum key distribution networks with resource
efficiency.
[0326] Referring now also to FIG. 64, in a nodal quantum key distribution
network, multiple trusted repeaters 6402 are connected via point to point
links 6404 between node 6406. The repeaters are connected via point to
point links between a quantum transmitter and a quantum receiver. These
point to point links 6404 can be realized using long distance optical
fiber lengths and may even utilize ground to satellite quantum key
distribution communication. While point to point connections 6404 are
suitable to form a backbone quantum core network, they are less suitable
to provide the lastmile service needed to give a multitude of users
access to the quantum key distribution infrastructure. Reconfigurable
optical networks based on optical switches or wavelength division
multiplexing may achieve more flexible network structures, however, they
also require the installation of a full quantum key distribution system
per user which is prohibitively expensive for many applications.
[0327] The quantum key signals used in quantum key distribution need only
travel in one direction along a fiber to establish a secure key between
the transmitter and the receiver. Single photon quantum key distribution
with the sender positioned at the network node 6406 and the receiver at
the user premises therefore lends itself to a passive multiuser network
approach. However, this downstream implementation has two major
shortcomings. Firstly, every user in the network requires a single photon
detector, which is often expensive and difficult to operate.
Additionally, it is not possible to deterministically address a user. All
detectors, therefore, have to operate at the same speed as a transmitter
in order not to miss photons, which means that most of the detector
bandwidth is unused.
[0328] Most systems associated with a downstream implementation can be
overcome. The most valuable resource should be shared by all users and
should operate at full capacity. One can build an upstream quantum access
network in which the transmitters are placed at the end user location and
a common receiver is placed at the network node. This way, an operation
with up to 64 users is feasible, which can be done with multiuser
quantum key distribution over a 1.times.64 passive optical splitter.
[0329] Thus, using various configurations of the above described orbital
angular momentum processing, multilayer overlay modulation, and quantum
key distribution within various types of communication networks and more
particularly optical fiber networks and freespace optic communication
network, a variety of benefits and improvements in system bandwidth and
capacity maybe achieved.
[0330] It will be appreciated by those skilled in the art having the
benefit of this disclosure that this system and method for communication
using orbital angular momentum with multiple layer overlay modulation
provides improved bandwidth and data transmission capability. It should
be understood that the drawings and detailed description herein are to be
regarded in an illustrative rather than a restrictive manner, and are not
intended to be limiting to the particular forms and examples disclosed.
On the contrary, included are any further modifications, changes,
rearrangements, substitutions, alternatives, design choices, and
embodiments apparent to those of ordinary skill in the art, without
departing from the spirit and scope hereof, as defined by the following
claims. Thus, it is intended that the following claims be interpreted to
embrace all such further modifications, changes, rearrangements,
substitutions, alternatives, design choices, and embodiments.
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